I haven't played either of these two games, but I've played their predecessors, and I assume that gameplay is largely unchanged between versions.
They're quite similar in that they're grid-based SRPGs, but beyond that there isn't much similarity. Disgaea will most likely have a more fun story, but you might not see much of it because you'll be busy grinding your ass off. If you don't mind grinding, Disgaea is a great big pit waiting to get filled with your time. Disgaea also has combo attacks when you align allies in certain patterns and crazy geo effects which complicate the battlefield. My beef with Disgaea is the grinding, which I am sick of, and how hard it is to level healers.
If you have a DS Lite, I strongly recommend you look into getting one of the GBA Fire Emblem games (the DS FE, Shadow Dragon, isn't as fun, but you might want to try it if you have a DSi with no GBA port). I've also found Valkyrie Profile to be a very fun SRPG on the DS and I'd recommend it over Shadow Dragon, too.

"The worst part about these reviews is they are [subjective]--and their scores often depend on how drunk you got the media at a Street Fighter event." — Mona Hamilton, Capcom Senior VP of Marketing
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