I personally prefer Aria of Sorrow (voted for it). I liked everything about it. The things I did like about Dawn of Sorrow were introduced by AoS.
Although DoS contains some of the best Castlevania tracks ever in my opinion (Cursed Clock Tower and Condemned Tower), I found part of the soundtrack lacking, especially at some of the first levels (not the first stage, which I really like), and, while a good track on its own right, I found the remix of the Haunted Castle track very out of place; while AoS's soundtrack was very good in general and included some rare gems like Study.
I loved AoS's story and I find the ending when Julius kills Soma as one of my favourite Castlevania moments ever. I loved the characters too.
DoS's story, on the other side, seemed pretty mediocre to me, and while it included the characters I love from AoS, I found the new characters to be generic and kind of "random".
In terms of scenery and look they are similar, and not counting that DoS was made for a technically superior portable console, I find it difficult to decide on this one. There was one stage I didn't like in DoS (the one with the ice blocks), but my favourite stages from both Sorrow games are also from DoS (Condemned Tower, Cursed Clock Tower and the first stage). However, I found DoS's castle in general to be kind of more of the same but with better graphics.
In terms of gameplay, I really liked them both, but DoS just used what AoS invented, and I didn't like the touch controls part (magic seals, destroying ice blocks with the stylus...).
So, in general, I liked everything more in Aria of Sorrow.
One thing that stands up for me with Dawn of Sorrow is the side quests (something very important to me in every Castlevania game). I really loved them, especially the ones about the supernatural newspapers. Sidequests is the thing I usually think of when talking about DoS. In this aspect, I think DoS established the ground for the far more complex, excellent PoR and OoE sidequests.