Go to the bottom if you don't want to read this...I think they both have their own strengths, and I think it really depends on how tolerant you are to either one's weakness as to which one is "better".
DAO suffered from some really, really bad balance issues that (for me) made it totally unplayable. These really weren't issues one could work around. These were design flaws in the way Abilities and Attributes worked for certain classes, and basically how functional each individual ability is.
Frankly, I never play "Caster/Mage" classes in these games, because they are never presented as anything interesting to play. DAO didn't deviate from this, thus I played a Two-Handed Warrior. Anyone who tried to play one of these knows - they just weren't fun to play because they were incredibly too slow and literally had nothing useful to offer the team. On top of this, I knew in the back of my mind that I wasn't playing poorly.... the game just simply fell apart for certain builds (namely Archers and Two Handed specs.) That doesn't mean you couldn't win - it just means you're basically fighting an uphill battle the whole way through. You always feel like... well... this build never makes you feel heroic in any capacity.
If I had to sum up DAO: it had slow and boring gameplay. Playing a Warrior in DAO has got to be one of the worst game experiences I have ever had. It really was that bad. How bad? Once I got Morrigan... I literally did nothing but control her, because my MC and Allistair basically played themselves.... with their 5 skills between the two of them that had seemingly 1 hour cooldown timers because I literally used them in a 20m fight once. Not that it matters anyway, because they never had enough Stamina to use them again anyway.... *shivers* It took a mod to get some stamina potions.... which are probably the single biggest oversight of the game if you ask me. But whatever -
Now, that's what DAO did wrong. I don't think anyone can really argue that point. If DAO had a bad aspect to it - it's that. And... well... DA2 pretty much fixed every bit of those issues. All the clases are a blast to play. They even did the impossible that no other game has ever done - they made Mages bad@ss! Are there some balance issues still? Sure - possibly. In fact, some people complain "Rogue/Mage/Warrior is soooo underpowered." Yeah, well, I haven't experienced any of that to a degree that is even remotely noticable. There might be some slight differences in power for each of the classes, but - I would take that over DAO's functionally useless builds/abilities.
Now, some people are going to complain about how DAO gave you all of these customization options, and how DA2 basically put it on easy mode. This.... is a lie. The depth is totally there in DA2. In DAO, you basically had one section of a class, and you pretty much went all or nothing into it. The only class that really gave you any kind of freedom of "choice" is (surprise) Mage. But even then, you didn't go halfway into one line. The "level up" process in DAO was like.... uninspiring. I didn't look forward to a level up, because I always figured, "Great! Another opportunity for me to be completely useless, while Morrigan/Wynn does all the work." Don't get me wrong, I don't mind that Mages in DAO were useful. I just think everything else was unnecessarily useless. To me, that's just poor design, which to me, makes for a poor game.
In DA2, on just about every one of my characters, I have abilities selected all over the place. I don't have to totally devote myself to one line or section. The builds are very versatile like that, because they each play off certain skills of another class. In essense, the "level up" is more about the team experience, rather than how awesome your MC is. And - the "level up" is FUN! You literally can sit for 30m-1h and think about what skill to get next; how will it play in the team you want to build; how is this point in one of your Attributes going to effect your game for the next couple of hours until your next level up? This is how leveling up SHOULD be. In DAO - there was none of that.
Now for me - these sorts of things are a big deal. I can almost completely forgive DA2 for the fact that it uses recycled environments (.... ALMOST

) for the simple fact that I am not going through the game feeling like I made a poor decision in wanting to play a character that uses Two Handed weapons. That sort of decision isn't something the player should feel like they are being punished for, for the entirety of the game. That's just silly. And that's exactly how I felt in DAO: I felt like the game punished me for playing one of the classes.
As far as stories are concerned... I really think DA2 had FAR superior things going on in this department too. I just feel like maybe it was less "epic" because of the recycled areas. In all honesty... that's really the only thing I have to gripe about DA2. I think every other aspect about it is a MAJOR imporvement over the first.
No armor selection for the companions? Who cares? Why is that even important? Can anyone explain why this is even necessary other than "It's how it's always been done."? It was awesome to see these unique characters being protrayed appropriately awesome all the time, and to see their gear become more ornate the better you got to know them.
Frankly, the only things I have seen people throw up (besides the recycled rooms) as to why DA2 is such a bad game are what I like to call "Non-Issues". Essentially, theses are tiny things that people blow way out of proportion to complain about, not because their complaints are necessarily valid, but because they just like to complain about anything.
DA2 is the suprior game in just about all aspects. The only drawbacks are the recycled envirnoment maps. I can understand that the need for this existed because the entire game took place in this one city. For story aspects, I can appreciate that. But in a game - it's kind of one of those things that sounds good on paper, but really isn't going to cut it in actual practice. What DA2 did here would be kind of like (back on the NES) if you were playing Mega Man - you went to Flash Man's stage, only to find out it was exactly like Fire Man's stage - with (maybe) different enemies. Bioware.... you can't do that and expect anyone to be okay with it lol.... That one feature alone nearly kills the entire game.
The second drawback are the sky-dropping-ninja-wave spawns of reinforcements! I.... honestly, this is kind of silly... but it's not really a game breaker for me. I mean... yeah... I guess it would be cooler if something else were to happen, but aside from guys just teleporting in, what else can they do? Tunnel up from the ground?
Anyway, my answer to this is: DA2 is the better game.