There was an interesting article in USA Today about three coaching "family trees" headed by (1) Bill Walsh (Holmgren, Dennis), (2) Parcells (Belicheck, Mangini) and (3) Schottenheimer (Cowher & I think Fisher).
I mention this in light of (a) an earlier post where I suggested that in a situation where the offense struggled but the defense was talented, a coach like Parcells or Belicheck would accept reality, pull in his horns, challenge his defense to play even better and opt to win boring 9 - 7 or 13 - 10 type contests, (b) a comment by Edge that "we're going to have to lean more on the Cardinal defense" and (c) DG's comment that "no, we can't ask our defense to do any more than they've been doing."
This illustrates the critical difference in the 2 coaching philosophies (Belicheck or Parcells would demand more of his defense).
Who would represent the ideal type of HC "after Dennis" is open to debate.
Right now, the Cards are on a high-powered offensive track. Prior to that, the Bidwills have experimented with the the nose to the grindstone style of Buges, the high risk/high reward style of Buddy Ryan, the low risk/low reward style of Vince Tobin, the high emotion/high effort approach of Coach Mac.
My conclusion - Don't worry about style and philosophy and focus on the bottom line - Go with the guy who knows how to win and has the consistent track record to show for it.
(Note - The guy could still be DG - He still has 12 games to save the season).