The First Doctor seemed like the type to fight regeneration - it actually surprised me that Twelve is the same. When they shot that very first regeneration scene, did they even have a name of it yet (regeneration) because I love the idea of the doctor refusing the loose his first face, his identity but then every incarnation since has embraced the act of regeneration even if they didn't want to change. Twelve really seems adamant about dying rather than regenerating though.
Interestingly, I had a long conversation with some friends the other day about another popular UK property - James Bond. I've always compared the two for being long running series which replace their titular characters actor - albeit in different ways. The Doctor is always, technically, the same character but changed his face in lieu of death; sacrificing who he is at that moment but continuing to do what the doctor does. While Bond is more ambiguous, different spies of different eras, given the same code (007) and I've always always assumed that they took on the moniker of 'James Bond' as their alias. But i suppose this is less likely and we're just seeing the same character (James Bond) played by different actors to tell unique stories and its not nearly as complex as my mind thought.