Maybe an aspect is like Bickle, but if you remember the end of the killing spree in Taxi Driver, Bickle was entirely unhinged. Castle is tactical, controlled, and never detached from reality.
Also BIckle's motivations are drastically different than The Punisher's. It's in those motivations, and exposition by the character, that the full form of the character is revealed.
Other than killing people, being ex-military and wanting to clear the scum off the streets, there's not much the same between Bickle and Castle. Their motivations are drastically different. Bickle is rejected by a woman and begins to plot to kill the Senate candidate she works for, for fame or attention....that's a world away from Castle.
He fixates on a 12 prostitute and kills everyone around here, almost in a trance at the time.
To me, characters are their motivations...what pushes them to act. These characters are so radically different in that respect it's hard to see that they are more alike than they are different.
Really, he's a hell of a lot more like Kersey in Death Wish, in terms of motivation, than Bickle.
Yea he doesn't remind me of Bickle at all in personality. Bickle wouldn't have been offended by that pawn shop owner mentioning the kiddie porn, but obviously Frank Castle was. Bickle was insane, Castle isn't. I'm guessing that the comparison is mostly coming from their appearance which is vaguely similar early in the show, particularly the jacket.