I've played way less than many of the others, but here be my preliminary thoughts:
Pros:
1) As mentioned, the Public Quest system is brilliant. It gives you the positives of MMO groups without the agony of pulling together 5 guildie folks or dealing with flakey pugs. It's also way faster rather than a 2-hour instance. I'm not sure if it's perfect yet: if you're a marginal player, you'll get way less loot out of PQs than instance runs (you could call this a plus because it eliminates the "free rider" effect you get in WoW) and the scoring may favor fast-killing DPS types over healers, tanks, and other support people. But it's awesome and I don't see WoW being able to replicate the structure anytime soon.
2) One of the coolest things about WoW, to me, is the serverwide events. Like the Gates of AQ, the scourge invasion, that kind of thing. However, they come pretty few and far between on WoW. It's an intrinsic part of the WAR system. The entire "war" between the sides isn't just some zone-specific stuff giving some marginal temporary stat bonuses ... it moves along the entire story of the game. And the notion of having city ranks and advancement makes this even more real. You advance your toon, your advance your guild, you advance your entire army/faction and each as specific progression.
3) I just mentioned guild ranks. Again, what an awesome idea. Guilds become more than just where they sit on WoWJutsu and what boss they took down, or how many recruits they have. And there are tangible benefits to progressing in terms of guild functionality. Again, awesome.
4) Character advancement is also way cooler.
In WoW, you have four individual things to advance: XP, faction rep, PvP honor, and Arena points. XP in WoW is great, no issues there. Faction rep is, well, either a gimme thing not requiring much thought that's a side effect of other activity (e.g. Hydraxian Waterlords or Violet Eye) or a horrendous grind (e.g. notably on the ridiculous Sabertooth Trainers). The PvP honor has gone through several reshuffles, but it's still just a grind. It's a little faster grind if you've got some skills, but lucking into a good team matters a lot more than having individual skills. Lastly, arena points ... I never touched this too much and it is clearly much more skill based and it's pretty cool for groups of 2-5 friends ... but still, it's both a grind and you're locked into weekly participation to "keep up." Obviously arena rank is a bit of a hybrid as it's really your team rank that you advance.
In WAR, you have three individual things to advance: XP, renown, and influence. XP is like WoW ... the one slightly nicer WAR thing is that you get XP doing either PvE or RvR stuff so if you really don't care about the PvE part of the game, you can advance and blow it off. Options are always good. But overall, not a big difference there. Renown is basically WAR's equivalent to honor points. It's way more thought out ... most obviously becuase there are ranks to it, not just a point total. It's also more balanced ... in scenarios (WAR's equivalent of WoW's BGs), if you're a great player on a lousy team, in most cases you can still build up renown more quickly if you've got skilz than if you don't. If you're a great player on a great team, you can advance it MUCH more quickly. There is also better functionality to support the scenarios in terms of being able to join as a group. Lastly (and perhaps biggest) ... non-scenario/BG RvR is well-defined. Open-world PvP in WoW never really has worked ... the best end-game part is probably Halaa and ultimately it attracts folks who like pwning others ... there really isn't an "advancement" incentive to do it. Finally, influence basically moves the "story" along in the game and you get influence by doing PQs. It's a little weird in that if you do any substantial amount of RvR you advance quickly enough that you end up ignoring the influence progression (too much content is a weird problem to have). There are consumable and gear rewards ... so by doing PQs you get may get gear rewards from the "drops" of each successful PQ that'd done (depending on your performance/contribution and /roll luck) but you definitely get gear rewards from accumulating enough influence if you grind them out. So overall, WoW is an XP-based game where reputation and PvP are kind of specialized addons ... in WAR, XP, renown, and influence are much more integrated and less grindey. The worst part about WAR is the naming convention ... renown and influence would be better called "Battle rank" and "Lore rank" imo but that's so trivial it's not worth talking about.
5) A lot of stuff that in WoW comes from addons (or on Web databases) is in the base interface with WAR. A lot more in-game info is available with WAR.
6) WAR has a very extensive titles system. On one hand, this is trivial (do I *really* need the option to call myself Squig Bait?). On the other hand, it's fun (apparently I do, because I do call myself Squig Bait). In WoW, there were very few titles but they carried much more meaning (e.g. Grand Marshall = I had no life in late 2005).
CONS
1) Even though the graphics are clearly a product of a "four years later" game with WAR than WoW, there's some roughness. The gamma levels especially can get you ... at night, often it really is dark so you can't even where you're going or what's lurking there. Either they want a little bit overboard on the RPG part there or it's just something that needs adjusting ... I suspect that it's the latter as it's way worse with a marginal graphics card than a decent one.
2) The action responsiveness also comes out in the gameplay/action. WoW is very responsive, I felt ... the cooldown timers and button mashing are all perfectly linked such that when you mash the button, it either does the thing or it gives you an error message. It's much mushy with WAR ... seems like I'm often pushing an action button early and it still does it. The actions are all slower ... I've heard that's intented to make fighting more "strategic" and less "twitchy" but to me it kind of is the difference between driving a loose-steering buick or a tight-steering bmw. It's not to the point that it's annoying, but it is different.
3) It's been pointed out that the texts are more integrated and meaningful, this is true. But ironically, I find myself reading the text quest much less often in WAR because it's, well, LONG. In WoW, it's much more compact, so it was easy to just scan it and get the idea of what Linkk wanted me to go fetch and so on. Maybe it's a function of it being the early days of a game where everyone is leveling is fast as possible right now, too, without "smelling the roses," but there's this bizarre situation where WAR does seem to have more deeply developed lore ... but I find myself ignoring it.
4) In the end game, the whole "faction balance" element is clearly a huge deal to WAR, and a few months from now that may be a big issue. It seems like the average server is at 60% Destro 40% Order. Will that mean that it's impossible (or very hard) for Order guilds to achieve end-game objectives? Will end-game objectives be boringly easy for Destro guilds? Who knows. It's not something that WoW had to deal with. Overall, Mythic has done some very ambitious things already -- just the 3-phase launch they did was incredibly risky and ultimately probably was about a "C+" in terms of overall execution at at times risked being an "F" [vs. their very ambitious launch plan ... it was an incredibly smooth launch vs. all typical MMO metrics in terms of server uptime, short login queues, etc]. So clearly they're not scared of the challenge. So far, I'm willing to trust that one way or another, sooner rather than later, they'll pull it off. But because the end game is dependent on player vs. player and group vs. group dynamics and not just PvE dynamics that the developer can tweak and control, it's a big and fascinating "if."
Gilga Wall of Text out (e.g., the boring conference call just ended).