The key difference, IMO, is that true agile doesn't require overt project management or more importantly, project managers. the usual response to the "wining battles, losing war" is to introduce someone who's keeping track. unless that someone is "everyone on the team", you tend to move away from agile because:
a)its not everyone's problem, so its not going to be fixed, or
b)the pm guy becomes the fountain head of knowledge from the pmbok that guide the "one true way"
if a project goes beyond a certain size, somebody has to be in charge. you could build, say, the Dallas Cowboys stadium, without a project manager who heads a project management office.
if your project is small enough that "everybody is in charge" and you've got the consensus to work that way you're not talking agile, you're talking magic... and you're going to be 3-10x as productive as a conventional "team"
a)its not everyone's problem, so its not going to be fixed, or
b)the pm guy becomes the fountain head of knowledge from the pmbok that guide the "one true way"