I think the biggest influence on wins and losses are injuries.
Now in the past I would have said players have more influence than coaching, but I'm swinging more towards coaching being a bigger factor.
Bad play calling and bad schemes are hard to overcome simply with talented players.
I think it is easier to do so on defense, because it is more reactionary. But playing the right scheme or calling up the right blitz or coverage at the right time is important.
On offense, the players are held solely to the discretion of the play caller. Each play - blocking assignments, reads, routes, all of it - are designed by the offensive coordinator. If that person can not figure out how to take advantage of what the defense is doing or is simply not instinctive enough to find a balance, then the offense will struggle.
Now, if the players don't play up to their potential, then coaching is moot. And I think that is a big part of team failure as well. Guys work hard and dominate in college. Get to the pros. Get a big fat contract and say "Why risk getting hurt? or Why try hard now that I'm a millionaire?"
So, I guess they all matter. It's a balance. Bad coaching can ruin a team, but a very talented team can probably overcome some bad coaching. A poorly talented team can win a couple of games with great coaching, but will almost always lose out to a more talented team.