These chords are a pain. I still don't always get a clean F major but I can do it a heck of a lot better than I used to. It just took a bunch of practice.

I still stink at the B but I use my first finger and my third finger. If I am on the same page as you it would be the alternate fingering. I do this only because my fingers are far to fat to get them all squeezed in there.

I play an acoustic and with the F I defiantly have to put down some pressure on the first two strings with my index finger.

I can't say for sure but I guess the alternate fingerings are good to know but I don't think you want to use one or the other exclusively. I think you want to try to get them all down so depending on where you are coming from or where you are headed you can be in position.