Is there a difference in image quality by rendering on different computers? I have two computers. My new one is pretty solid, but it still takes 8 hours to render 3 seconds at 24 fps. I wouldn't mind it but i have other things i want to use that computer for in the meantime. 

If i were to transfer the project to my old computer could i let it render non stop (for like a week)? Would it look any worse? I know it would take longer, but i don't really mind as long i can use my new computer without a major handicap.

I don't have the old one on me at the moment but from what i can remember it has

6gb of ram

core i3

nvidia gt 650m

EDIT: it's in cycles
No. The only thing that will change is the rendering time, everything else should be exactly the same.