I feel like Phil took this job for multiple reasons, one of the biggest being that the Lakers snubbed him for Dantoni.
Basically, the question is Phil's philosophy vs. Dantoni's philosophy. Dantoni's European flavored high P&R, free flowing, point guard driven, three point shooting offense currently dominates the league. That is why Phil mentioned copycat league when talking about potential coaches. The triangle is a system of movements that are scripted for the first couple and improvised based on the defense's reaction. It is a series of cut/passes and picks from different angles simultaneously (like any system offense). If you study film, play a lot of it, and execute your movements over and over again you start seeing tendencies of your teammates, moves that work consistently and so on. It allows for lesser talented role players to be maximized as opposed to functioning as merely a court spacer.
It seems as if Phil is out to prove that his philosophy wins championships while Dantoni's philosophy is a mere gimmick and that the Lakers will regret choosing against him. When the Lakers chose Dantoni it was like a stab in the back! It was about more than just choosing a different coach. Back when the Lakers and Suns were squaring off, it was bigger than two teams it was two styles of BBall squaring off against each other for league supremacy. Phil won the battles but lost the war...for now
Woodson, employed Dantoni's system by default but didn't really understand or ever feel completely comfortable with it. He used it by mistake in 2013 until he couldn't take it anymore and reverted to what he knows vs. the Pacers, and he abandoned it completely this season. The players sensed his internal conflict, didn't buy in and the rest is history. Woodson, didn't seem to stand for anything philosophically, hence he fell for nothing.
Now, we get to see if system Bball is truly dominant. I think if given equal talent, system wins vs. Dantoni ball. I am curious to see how this plays out.