This is not such an easy question. It has pit falls in it.

While the situation is theoretical the conditions are:
Original band project given a choice:
A) School trained musician with all the theory and all the mechanical skill, an excellent performer, but lousy at composing anything at all. All his compositions sound "over thought" "too technical" "tasteless"
B) Self thought axeman, does not know theory, can read a TAB on a good day, but can play by ear and play very well. All from the feeling, every bit of it, without knowing why he does it. However his answer to question: "please play me Half Diminished (Locrian) scale in A#" is "huh?"
It would seem that if you are writing music and need performer you go for A while if you are in need of input in creating music you go for B. Remember: they are both good at what they do.
Therefore an odd
possible paradox: A School trained musician ends up playing in cover bands and/or for untrained musicians who created that music in the first place.
*edits
gtZip -
no we are not talking about me. It is a
hypothetical and perhaps
unlikely situation where one would be given this exact choice. A loaded question to get your brain going.
Matt F - I am not saying that trained musicians suck. Of cause it is no brainier if you can choose a trained musician who is also a great composer but that was not the choice in the original post.
SlippedNot - choosing the guy 'B' may seem like a logical choice, yet that may be that pit fall I am talking about. You are experienced musician I have a lot of respect for you. Let's play a devils advocate. What if you do not care about his ability to improvise and you are on a tight schedule? Would you still take the untrained guy? They both can shred that fretboard, one will do like you tell him to, the other is how he feels it (both consistent all the time). Both excellent players though.
Hayden King - very eloquently put. However I am not given that choice. Lately I am given a choice between a drummer who can't play drums and bassist who can't play bass. I was lucky to meet a guitarist in my area here on this site who is BY FAR better player then I ever will be and him and I are working on new stuff now. Personally, if I would be formally trained I would take a schooled craftsman and so I can give him a piece of paper with my music on it and let him have at it. But since I can't write that piece of paper in the first place, his ability to read it means nothing to me. I am not that caliber.