AoS is a significantly better game. I'd pick the first one any day of the week over the second.
That's not to say that the second one is bad at all, though. Sure, it's got some crap, like:
-The story was a needless continuation to the otherwise perfect ending AoS had for the series
-The story itself was terrible, with all the new characters sucking really bad (well, aside from Dario. I actually liked him)
-The artwork being downgraded to what is famously referred to as "generic Saturday morning anime"
-The characters themselves being downgraded to what is "generic Saturday morning anime"*
-Terrible and needless implementation of touch-screen gimmickry (magic seals, ice breaking, etc)
* = Characters weren't deep or fleshed out in AoS, but at least they didn't have pointless quirks, like Hammer's weird and random schoolboy crush on Yoko. He mentioned being attracted to Yoko in AoS, but he was more smooth and mature about it, and the game didn't make a big deal out of it. DoS turned him into a real kid about it, and the game constantly brought it up to the point where it was annoying.
But it did have some cool stuff:
-Gameplay, aside from touch-screen gimmickry, was great
-Collecting multiples of the same soul powers up said soul
-Julius Mode having a story to it. Sure, it's barely there, but it sufficed and was pretty nice
-Julius Mode having two other playable characters to use
-Julius Mode having a leveling system, rather than just being the same throughout the game
-Larger and more varied environments
-Another excellent soundtrack
Overall, though, it felt like they were just doing a DS remake of AoS at first before changing it last minute to be a sequel rather than a remake. You're repeating a lot of the same stuff as you did in the original, albeit slightly changed, but the game's plot still revolves around mostly the same thing, along with the fact that you're doing a lot of the same stuff you did in AoS.
tl;dr - AoS is much better, but DoS wasn't too shabby.