But on this very site, pre Iron Man release SHH had their interview w/ the director and he mentioned Batman Begins numerous times as being a source of inspiration.
The MAN OF STEEL I don't think has had any direct quotes relating it's influence to BEGINS, but it's obvious. The think tank for the film was Goyer and Nolan. And even the text of the film's title is in the same font and style of BEGINS, TDK, and RISES.
Amazing Spider-Man has obviously been fashioned after BEGINS. The Raimi films, much like the Burton / Schumacher films were more stylized fair and done with tongue in cheek, that eventually went down a road of colorful camp.
Amazing Spider-Man is a grittier, more character study of Peter Parker akin to Batman Begins was with Bruce Wayne. Both franchises picked an actor who better suited the protagonist physically, and from an acting perspective. Both franchises were re-invisioned by a director that wasn't typical for that type of movie.
The inspiration is clear as day.