There are very minor differences between them... e.g. Some FRs have angeled fine tuners so there'll be less chance to touch them when you're palm muting... My FR doesn't have angeled fine tuners, I even place my palm over the tuners for some vibration , and my tuning never seem to change a bit.
If the FR II fits in your guitar without having to drill in your guitar body get it...
I don't understand what do you mean by "non-finetuning" anyway , but if it ain't FR , I guess you'll have to dig in your guitar body for it which is something I don't recomend.
