Just because he has similar strengths/weaknesses doesn't mean he'll coach the same way. I wouldn't avoid any defense-oriented coach just because Woody was one. His coaching style, demeanor, locker room presence, decisions, etc. could well be very different than Woody's even if they have similarities. Not saying he's the guy to get, as I don't know much about him, but I don't think it makes sense to rule him out for that reason.
What if we hired someone that was the opposite, an offensive-minded coach that rides his team in the games and in the media? He'd be different than Woody but a season later you'd start hearing how we need to concentrate on defense and so on.
While we're talking coaching arguments, how about the one where we should only get a coach who has taken a team further into the playoffs than we've been? Are we limited to only picking coaches who have been in or won the Finals? I'd rather be the team who makes a smart pick and gets the next coach that will make an appearance there.