Where did it indicate he travelled the world learning from different people in different aspects? All we know is he went somewhere in Asia and was a thief. Then ended up with the League of Shadows and Ra's.
What detective work did he do?
Also i never really got the sense he was obsessed or that determined outside of Begins. After that all he wants to do is retire as Batman, finding someone else to take up his mantle. One of those guys in Harvey Dent. So Bruce wants Harvey to become the White Knight of Gotham so he can retire. And he is actively trying to win over his girl, Rachel Dawes. Nice one Bruce. What an *******. Very noble.
The other guy he wants to take up his mantle is an untrained (in terms of you know, being Batman) rookie detective who figured out Bruce was Batman because he could see anger behind his smile... the entire Batman legend is left in his hands whilst Bruce pisses off to Italy with some girl he barely even knows and who isn't exactly trustworthy. What a totally Batman thing to do! Oh wait... him sticking around after faking his death to train Blake would have been what the definitive Batman would do. And also, thematically interesting because it does bring it all full circle, with Bruce taking on the role of Ra's. There is a whole fatherhood theme there too.
What exactly did Nolan do better or different to the comics when it comes to Batman's existence being necessary? Gotham has always been portrayed as corrupt and a city of sin in the comics. With cops, judges and politicians on the take. Mob wars. Nolan didn't bring anything new to the table there. Although he did tell a really great story in TDK featuring those aspects. Most definitely.
You can't just pick and choose all aspects of the characters. Otherwise it doesn't really become that character. The comics should always be respected because like i said, at the end of the day, it's the comics and their characters and the rich histories that inspire the film makers in the first place.
I'm not saying 100% accuracy to the comics. I totally understand some things don't work in films. I totally get that Nolan's version is a valid interpretation. And don't get me wrong... i think TDK is amazing. Begins is also great.
But a Batman who is frankly, a ***** hole who is constantly looking for a way out of his crusade because of females... is definitely not the definitive Batman.
Doctor Octopus more or less summed up what I would have said in response, however I'll add something. Whether someone likes how Nolan interpreted Batman is entirely up to them, but if the thing someone took away from the series was that Batman was a weak coward looking to bail then I've got to seriously question whether said person paid attention to the movie. Honestly, I can't see how any self respecting fan of the character can come to that conclusion.