The only thing they have in common is D&D. For the rest they’re completely different games with almost no overlap at all.
DDO is a very MMOish general quest game with dungeons that feel somewhat DM led, and Neverwinter is more an action adventure RPG with a… Rather annoying underlying real money/shop/collection mechanism.
Both are Free 2 Play, so I would say, try them both.
Yeah, you’ll know within a couple hours which one is more your style. Both games have an unfortunate amount of “look at what you’re missing!” If you’re playing for free. I found that Neverwinter had a lot more content available to a free player, if that’s a deciding factor.