I think people are looking at this from the wrong perspective. So much of the question posed depends on where your football and basketball program is at the time. An NIT championship although nice would be a retrogression of the basketball program from the point it is at. After 4 straight NCAA appearances, anything NIT related would be a step down for Alabama. For that reason, I would choose a mid tier bowl win.
A better question would be between a Final 4 appearance and a BCS Bowl game appearance (not the title game though). That choice would be easy for me. I choose the Final 4 seeing as that is the only major accomplishment in a major sport that we have yet to accomplish. We've been to national championship games in football and have even been deep into a few College Baseball World Series. The only other thing besides that we haven't done is actually win a College World Series. For me, I want Bama to at least say it has been to a Final 4.
A better question would be between a Final 4 appearance and a BCS Bowl game appearance (not the title game though). That choice would be easy for me. I choose the Final 4 seeing as that is the only major accomplishment in a major sport that we have yet to accomplish. We've been to national championship games in football and have even been deep into a few College Baseball World Series. The only other thing besides that we haven't done is actually win a College World Series. For me, I want Bama to at least say it has been to a Final 4.