Easy choice for me.  I'd stay at BYU.  I love football.  I was never BYU good, but I got I did have an FCS school and several lower division schools interested in me.  I actually chose to go to BYU instead of playing  football at a lower level.  It was a hard choice, but for me it was definately the right choice.

While I love football, particularly BYU football, there are still some things that are more important than football.  There may not be a very many, but your education and the personality, character, and habits that are formed during the college years are one of them.  BYU was an awesome place to go to school and definately shaped my life for the better.

I would happily be a 3rd stinger on BYU's team rather than transfer to a school that can't offer the BYU experience in an attempt attempt to get playing time against inferioir competition.

But everyone is different.  If I thought I had NFL talent and wanted to be a professional football player, I would probably transfer to find a place to showcase my abilities.