Lots of good advice in this thread. I began as a classical guitarist, and so I learned to barre the F chord with my first finger -- no exceptions, no excuses. But there are enough good guitarists who play the "thumb over" approach that I have to recognize it as a legitimate thing to do, my early training notwithstanding.

Ergonomics are an important, and often ignored, consideration in playing any instrument. Rick made a good point about a lot of this having to do with your wrist. Basically, if you're planning to do a first-finger barre, you need to make sure you're holding the instrument with the neck up high enough to accommodate this. This is a big part of the reason classical guitarists (who actually pay a lot of attention to body positioning) typically rest the instrument on their left thigh -- it brings the neck up, allowing your left wrist to stay relaxed, and making a first-finger barre much less work.

Conversely, if you plan to use the thumb-over approach, you need to make sure you're holding the instrument with the neck down low enough to accommodate this -- otherwise, again, you will be forced to contort your left wrist unnaturally. You will see a lot of low-slung guitars on rock and blues musicians, many of whom prefer the thumb-over approach; whether they started with the low-slung guitar to adapt to their hand positions, or vice-versa, it makes sense.

BUT, if you initially learned your hand positions from your classical guitar studies, and then started playing your electric slung low (because it looks cool, you know), you'll end up with an unnatural arch in your left wrist. This is an invitation to carpal tunnel syndrome (the voice of experience; trust me, you don't want to go there).