Having recently quit playing DAOC after about six months and starting up on FFXI, I'd have to say DAOC is better, although more tedious when it comes to PvE.
The conning system is much better. I don't know what it is with FFXI, but the check system is just horrible. Monsters vary wwaayy too much in strength from what I've seen. DAOC tells you what con the monster is to you as soon as you target it. It also tells you whether the mob is aggressive, neutral, or friendly. Targetting is much more simple, and when you're fighting a monster, it's a lot easier to switch to another mob if necessary. It's a better battle system in general, but as I said, very tedious. I got two of my characters up to level 50 and pretty much had my fill of PvE.
Bhodisattva's post is a little off. Necros happen to be the best PvE class in the game for solo play. Any other class, grouping is quite necessary in order to level up QUICKLY (in caps because it's an operative word..). With most tank/archer characters, you have to have someone that can give you endurance (endurance is what you use to use weapon styles..As opposed to FFXI where you can just sit there and auto-fight, if you're not using a weapon style in DAOC, you're not doing **** for damage and you're going to die in most instances.). Healers are also nice. Healing or buffing characters tend to lack the physical brunt to do their own killing (most of them can't use weapon styles), and as such will kill very slowly without some sort of help. Magic using characters can do well, especially if they're a pet class, but they tend to run out of MP quickly, and it takes a loonnggg freaking time to get your MP back in DAOC.
The actual partying system on DAOC is much better as well. You don't get kicked in the *** nearly as hard for partying and not being this super efficient well lubricated machine. Like for instance, most of the newbie parties tend to evolve by being in the same place at the same time. You might not level as fast as you were solo, but unless the XP is REALLY bad, you're probably not going to even notice a difference, plus you'll have this guy to talk to while you punch the buttons. Also, powerleveling is a lot more rampant in DAOC. I've gotten people from ~25-38 or so in a day by PLing them with a Champion.
For solo characters, Albion, you definitely want to go necro. Minstrels are good soloers too, but seriously, best character in the game for PvE is Necro, hands down. It's silly to choose something over it if you just want a PvE character. For Hibernia, Champions or Wardens tend to do best as solo artists. Wardens are verrryyy group compatible as well. Champions are the best PvE tank in the game. Light specced Mentalists can do decently as well, but it requires a lot of knowledge on how to play them correctly. For Midgard, you're probably looking at either a Bonedancer or a Spiritmaster. Bonedancers are great for solo play, but can get a little scary sometimes. You have to replace their equipment often (this depends on your spec..I'm not getting into that because there's a billion different opinions on how to spec your character). Spiritmaster pets are pretty cool, and they have something called PBAE magic that does a ton of damage, but requires you to be within melee distance of the target pretty much.
For FFXI, red mages are pretty nice when it comes to soloing, although they get expensive as hell down the line. It should be pretty easy to get one to 30 though, since they get parties a lot and for the first 20 or so levels you don't even have to party if you don't want to. I'm not promising it won't be frustrating at times, but like I said, you don't have to party if you don't want to. :-P
I've got to say though. If you don't plan on ever joining a guild or whatever in DAOC, I wouldn't bother wasting your time. PvP, the game's main selling point, is NEVER 1v1. Not any of the good stuff anyway. You're generally going to be looking at 1-3 full groups (8 - 24 people) for the fun stuff. Even most stealthers at least duo. It helps a lot to be with people who know what they're doing and you play with regularly as well.
I don't mean any disrespect to McHecker on this, but TOA is highly overrated for the most part. It's kind of the flavor of the month excuse as to why so-and-so is beating the **** out of whoever. There are a few skills that TOA can give characters that are highly useful, and some of the artifacts are good, but for the most part, it's fluff. Overall DAOC is a very balanced game. People that lose often either don't understand the dynamics of their realm's group compositions or just don't know how to work together well enough. I know in my old guild we could generally take two groups of albs or mids with just one group of our guys. It wasn't because hibs are overpowered, or we're all TOA'd out (we aren't..The guild as a whole is like ML6ish officially, or was at the time..I was ML2. :-P), or cheated (we pride ourselves on not using radar. ;)), but because we all worked together, and we were good.
Anyway..I've succeeded in making myself tired, so I'm going to quit ranting. :-P Have fun reading.