I've been convinced for a fairly long time now that the single most important in-print product for D&D is the Introductory Box. The future of most rules material seems to lie online, either through the DDI or through the use of eBooks or the like - basically, the ability to carry an entire library of materials on a smartphone or similar, coupled with the easy ability to reference such books, would seem to outweigh most other concerns. (Indeed, it gets to the point where DMs should strongly consider disallowing any materials that cannot be easily referenced online.)
However, the game needs new players, and needs them in large numbers. And online materials make for a really poor introduction to the game. Additionally, the core rulebooks of recent versions of the game also make for a very poor introduction - they typically run to 1,000 pages of text (or as near as makes no difference), and although we know there's no need to read all of that before play, a new player does not. Hence the need for a really good Introductory Box.
(Actually, ideally, the core game would be sufficiently simple that the Introductory Box could serve as the Core Rulebook for the game, with all expansions then building from that. Unfortunately, it looks like WotC, not to mention the community itself, are absolutely wedded to the three-book model, despite that it's probably killing the game. But I digress)
A few months ago, I picked up the starter sets for both 4e and Pathfinder: the Red Box and the Beginner Box, respectively. And, until last Friday, they were happily sitting on my shelf, unread. My reading of reviews online had given me a strong impression of both, but I hadn't actually gone through them, so couldn't really speak from a position of knowledge.
That changed on Friday. And so, here are my impressions:
First, let's dispense with the peripheral components, of which there are several.
On opening both boxes, the thing that is immediately noticable is a bag of dice. These were inevitable, and pretty dull. Both sets include a single set of the standard polyhedrals. I was a little surprised to see that the Red Box didn't include a d10 with the 10's marked... until I remembered that 4e doesn't actually use d% anywhere in the rules. Otherwise, there's nothing to separate the two sets. (One criticism I have of both is that the dice are all of one colour - all red or all black. I've found that colour-coding the dice by type has a surprisingly large impact on the speed of play, and especially for new players. Still, a mismatched set would be significantly more expensive, so...)
Both boxes also include character tokens and a battlemat. In the case of the Red Box, these consist of the traditional "pog" tokens that lie flat, and a paper battlemat with scenes printed on both sides. They're nice, and functional. In the Beginner Box, they have instead included thick cardboard "pawns" and plastic bases, giving a more 3-dimensional effect. Additionally, the battlemat is printed on thick card, with one side showing a dungeon scene and the other being blank (and suitable for marking with either wet- or dry-erase markers). In terms of the tokens, there's frankly very little difference - my preference is for the pawns, but it's a marginal thing. However, the Beginner Box battlemat is clearly the better of the two - both because it is sturdier, and also because the blank side provides better opportunities for reuse.
Both boxes also provide a small number of blank character sheets. In both cases, the sheets are fine, though they lean rather towards the "spreadsheet style" of all post-3e versions of D&D. That's a weakness in the game, though, and not something that these boxes could fix.
The first key area where the boxes diverge comes here. The Red Box supplements each character sheet with a set of power cards, providing a nice, if limited, set of powers for each class. These are a really nice addition; it would have been good had the Beginner Box been able to include spell cards.
Conversely, the Beginner Box provides character sheets for four pre-gen characters, one of each of the "big four" classes. However, these are not simply pre-filled character sheets - in each case the sheet is presented at the centre of a four-page spread, with the borders being used to explain key sections of the character sheet. This is a spectacularly good idea. Hopefully, when WotC do the 5e Introductory Box, they'll do the same.
Each box also includes a couple of flyers, giving instructions on how to use the set, links to further materials, and the inevitable adverts for the 'real' version of the game. Nothing much to see here.
So, until this point, there's really not a lot to swing it one way or another. The Pathfinder box has a slight edge in terms of content, but the D&D set has a big advantage in terms of cost (since it costs half as much). And, in each case, there are some components that may see reuse - dice, tokens, and battlemat.
And now we get to the 'meat' of the products: the rulebooks.
In each case, the sets include a Player's Book and a DM's Book (though they may not be called that). That's about as far as the similarities go, though.
The Red Box Player's Book is a 32-page "choose your own adventure" book that also doubles as character creation rules. You step through a very simple adventure about goblins attacking a caravan, and the decisions you make define your character - if your first impulse is to cast a spell, you're a Wizard... and so on.
This is okay for first use, but not so good beyond that. Once you've created that first character and need to create your second, you don't really want to be attacked by goblins again. And that's the extent of the Player's Book.
I have one other key criticism of the Player's Book, and the Red Box as a whole - when discussing actions that characters can take, there's a very distinct emphasis on using the power cards provided. You're expected and encouraged to stay "on book". But, of course, one of the very significant (and generally unfair) criticisms of 4e is that locking down all those powers stifles creativity by causing players to fixate on the cards. It was a real shame to see the Red Box explicitly encourage this.
The DM's Book picks up exactly where the other leaves off. It presents the DM with a starter adventure, then quickly presents the rules of the game, then presents another adventure, some monsters, some treasure, and then it's done.
I don't really have any great criticisms of the DM's Book. It does its job reasonably well. The end.
Where I do have a significant criticism of the Red Box is that it provides rules for levelling up the characters created, but only to 2nd level. Basically, it's a set that's good for three or four sessions, if that, and then you have to advance to the 'real' game.
Oh, there is one other criticism I would level: the adventures are presented in the now-defunct "Delve" format - every encounter area is presented across two full pages. This makes adventures easy to run, there's no denying. It also means that that first adventure takes up 14 pages - a crippling blow when space is at a premium.
By contrast, the Pathfinder books are much more what I expected from my experience with the old Red Box - the Player's book opens with a very short "choose your own adventure", then presents character creation rules (with 3 races, 4 classes, a limited set of skills, feats, and spells), rules for levelling up, combat rules, and so on.
The DM's book is likewise as I would expect - a couple of pregenerated adventures, a limited bestiary, some magic items. It's all laid out concisely and clearly, despite the greater mathematical complexity of Pathfinder over 4e.
Simply put, the Pathfinder box makes much better use of space, with the consequence that the box includes rules for advancing as far as 5th level - the set is good for several months of play.
But... the Beginner Box commits what I consider to be the cardinal sin of designing an Introductory Box. Because of the space constraints, it is inevitable that the box has to include a cut-down ruleset, and so things like disarm, sunder, and grapple are omitted. That's fine - there's nothing wrong with a cut-down ruleset. But what it should never be is an incompatible ruleset. A player who has used the Introductory Box to learn the game should be able to sit down at a table with a group using the 'real' version of the game and understand what's going on; he should not have to unlearn what he has learned.
But the Beginner Box omits attacks of opportunity (good idea), but does so in a manner incompatible with the 'real' game - moving past an opponent is unimpeded. Fixing this would have required the introduction of the five-foot step into the game (itself a weakness of post-3e D&D, but that's an aside), but failing to do so is a major weakness in the box.
(In fairness, I should also note that the Red Box contains a handful of discrepancies with Essentials, and of course several of the powers have since been errata'ed. However, the differences here are rather more minor.)
Conclusion
Ultimately, both sets aim to do the same thing, and they do so in extremely similar ways. It is the details of how they go about their task that are key.
And in that regard, the Pathfinder Beginner Box simply blows the 4e Red Box out of the water. By making better use of the space, and thus being able to present the game up to 5th level, they've provided a set that allows new players to get really comfortable with the system before they have to upgrade, and face up to those 1,000 pages of reading. By contrast, the Red Box is very much a "pay-for preview" - it's a product to be used a couple of times and then discarded.
This is not to say that the Pathfinder set is perfect. As I noted, it commits one of the cardinal sins. Additionally, it is rather hampered by the high level of complexity of the 'real' game itself - it was always a really big ask to present a coherent Introductory Set when the core rules run to nearly 1,000 pages.
(My overwhelming impression of the Red Box, as with the DDI, and as with 4e itself, is one of disappointment - not at the quality of the product itself, but that it represents such a missed opportunity. Until the Pathfinder set, the game hadn't had a really good Introductory Box for decades, and a really good set could have done wonders for the game. As it is, this wasn't that product, it failed to recapture the millions of lapsed gamers they wanted, and now the opportunity is lost.)
My final thought is this: if you have a young relative who you think might like the game (a nephew, say), the best way to introduce them to the game remains to do it yourself - teach them the game yourself, take them through some introductory adventures, and then ease them into a group. And, of course, the game to teach is the one that you prefer.
However, if life doesn't permit you to do this, then an Introductory Box is the next best thing. And here, my recommendation is clear - get the Pathfinder set.