In my opinion, with caveat that you can manipulate a Head Coach with your Gameplan construct.
Possession: Is a risk averse Coach who wants to dominate the clock. He'll want to run up the gut and throw short safe passes to keep the chains moving. When given options, he'll be less likely to try and throw the ball deep.
Generally Balanced: Your HC ideally wants a wide mix of plays and will want to see a 50/50 split between running and passing. He is also more likely to take shots/gamble than a Possession philosopher.
Run Biased: A conservative who wants to ground and pound and wear down his opponents Defense. Generally suited to a physical, strong Offense.
Pass Biased: More likely to throw on first and second downs and will look to stretch defenses and test the other teams secondary in both coverage and pursuit. Should suit a team built with a speed kills mentality.
West Coast: I'm never really sure about what the West Coast offense is trying to do, I would say it's a similar philosophy to Possession but they want to throw more than run. Short safe passes and outside runs. I would imagine he'll be looking to run more misdirection plays, play action passes and get his playmakers into open field situations rather than being physically dominant.
Like I say though, you can push a Coach away from his preferred style with how you set up your play choices, gameplanning matrix and rules. When left to AI control they will default back towards these options (although I think they are all too risk averse in the default settings)
