I am new to the Fallout franchise and I am currently on my first play through for FO3 GOTY. I've read that FONV is a different game, more about choices unlike FO3 which focuses more on explaoration. My question is, if I start FONV UE, will I spoil anything for FO3 or should I just wait until I finish FO3?

Story wise you won't spoil much.

Gameplay wise though...

So I would be good with a similar build for FONV focusing on VATS perks?

Not necessarily. In New Vegas you only get a perk every two levels, as opposed to one perk per level in Fallout 3. So your characters will progress differently in each game.