From what I understand these are two mods which can be considered the closest thing to an "Unofficial Patch" for Fallout New Vegas. However when I was browsing around the internet I saw mentions of how Mission Mojave is a bad mod that contains many undocumented and unnecessary changes to the game and how the Bugfix Plugin for NVEC is much superior as it doesn't touch upon any gameplay elements.

For someone who already has a one hour gaming session with the MMUI mod would anyone suggest that I delete it and create a new character with NVEC instead? Also does anyone know anything about those undocumented changes in MMUI, for instance what they are? And which of the mods do you prefer personally?

I suggest YUP for bug fixes. MMUE has a lot of changes that shouldn't even be included in there and it's plus edition which is an add-on to it combines smaller mods. NVEC has several different modules I suppose you could call them. It has a bug fix, and enhancement with bug fix and enhancement with bug fix and a face fixer.

I am personally using the enhancements and bug fixes along side YUP.