Best I can tell, the larger one is a bowl gouge with a "traditional" grind, and the smaller one is what I'd call a detail gouge.
I've not really used a traditional grind on a bowl gouge much at all, so for me, I'd probably re-grind it with more of a fingernail profile. The fingernail profile is generally considered to be a bit easier to use, and it's also more versatile...you can do several different cuts with the same gouge. Others, though, prefer the traditional grind, especially when working on the bottom of the inside of a bowl.
The profile on the detail gouge is similar to what I use, although I have the wings of mine swept back a bit farther (a bit more fingernail-ish than yours is now).
Since you're just starting, I'd suggest re-grinding the bowl gouge to have more of a fingernail profile, but I'd leave the detail gouge as-is for a while until you've used it a bit. As time goes on and you gain more experience, you can change the profiles of either gouge to fit your preferences. (And that might take several different iterations in order to find out what your preferences are.)