Dawn of Sorrow was essentially a mechanically perfected AoS. If you liked the soul mechanics introduced in Aria (or just like Soma in general), DoS is your obvious choice -- it adds soul leveling, and comes with a nice "soul synthesis" mechanic (soul-based weapon crafting). Also, DoS Soma is arguably the better sprite (although Dawn completely kills Julius').
Since you've already played Aria, you should probably know the Sorrow soul system is one of the best abilities system in the series. Which means that DoS easily trumps Portrait in terms of unique abilities.
You'll also find some great nonlinear level design, as well as a few interesting boss fights. And like PFG mentioned, DoS is more stable in terms of atmosphere than PoR.
But if you want some classic whip action... Well, DoS doesn't have much to offer. Sure, it has its Julius mode, but the main game has you stick with Soma's diverse but whip-free weapon set. And especially if you're looking for a more classic CV... DoS is as Metroidvania as it gets. It's one of the best, but be forewarned.
Also, you should only take on DoS if you know you can stand the atrocious story and artistic design (and, to a lesser degree, the touch screen gimmicks). Those are the only drawbacks, but they're beyond bad.
Choose Portrait of Ruin if you want some classic Belmont gameplay. Jonathan isn't a Belmont per se, but he apparently shares the family's blood. You'll find some great new whip designs (think Nebula), as well as a mind-blowing selection of subweapons (all of which can be leveled and mastered). You'll also find an enormous selection of weaponry, along with a monumental variety of spells (all of which can be charged), along with a dual crush mechanic, along with a large variety of equipment that'll fill eight slots for each character -- essentially, if you want the largest arsenal you'll have ever seen in a handheld Castlevania game, go for Portrait of Ruin.
Portrait of Ruin also comes with a dual-character system, which is both a blessing and a curse. It's nice to be able to handle to different characters, each with different playstyles -- you can even have them both on the screen at once (if you can handle the touch commands). But there will be moments where you'll start wishing that you were only given a single character -- having to switch between the two for more effective weapon usage can easily become tedious.
This game's level design is interesting; it's more linear, more streamlined, but the portrait system allows you to travel through a fascinating variety of locales, including two particularly fascinating stages (get to the Nation of Fools, and you'll know what I mean).
The storyline is decent, with Brauner as one of the more fleshed-out villains of the series, but the game's artificially light tone is almost a dealbreaker here. Cutscenes between Jonathan and Charlotte will have you cringing every time you hear "no problem" or see an angry face (it's legendary).
Both games have decent music, with DoS boasting a few memorable tunes, while PoR benefits from a strong overall soundtrack (even though not much stands out).
In the end, of course, it's entirely up to you.