I said GM but alot of the time you have HC's acting in a defacto GM role, bring in "their guys". I think whoever has final say over the personnel decisions on a team is the most important.
I'll go with the GM. You can compensate for any weaknesses a head coach may have with the coordinators and position coaches. A bad GM will totally screw up a franchise in just about every way possible.
What the hell does a GM know about football? Most of these GMs are just rich fuckers that wanna sit there and inherit more money.
A good coach can face a GM. And even if the GM is a brick and can't manage his cap for shit, a good HC can make up for it by playing his players right. A GM can't do shit with an incompitent coach. Example, Gruden winning SB 37 before McKay ditched and left a HUGE cap mess with all the backed up contracts he signed players to while he was here. Now he's in ATL, and I just laugh at the thought of Vicks 10 year 100 mill contract.