NGB is completely optimized for XBOX. Runs and plays very smoothly. Has a lot of content (some removed in NGS, you have to look them up I don't remember). It's amazing from Team Ninja did with NGB and XBOX specs.
NGS is essentially a remastered HD, but the problem is the game has occasional in game loading - meaning, you are traversing one area from another like an open world, but for some reason the way the game was engineered, sometimes the game will literally pause and say "now loading," even when enemies are spawning. It's kind of hilarious.
NGS added playable character in Rachel, who is not really fun to play. And (this is not without googling) I also believe NGS is made a tad bit easier and more accessible...which some people find a turn off.
Personally, NGS is just fine, especially with its remastered HD graphics. It's quite stunning running 720p (i think it did 1080p also?) and 60fps and watch Ryu just killing fools. Oh, but NGS retains XBOX, low-res FMV.
Like this
Basically, if you can play NGB, that's the definitive version - all the extras in NGS does not make NGS better.