Che and Crash are dramas and both are not independent movies in my opinion (Soderbergh, del Toro, Haggis, Dillon, Bullock, Cheadle involved - these established Hollywood names definitely helped funding the movies). "Das Boot" is definitely not an independent movie, 28 years after its release it's most probably still one of the highest budgeted German movies ever made. But what are real independent movies anyway? Troma's movies definitely, Roger Coman's maybe...
@canch: Don't you think you meant pure popcorn action movies vs. drama movies with some action? Or generally superficial vs. more realistic?
Regarding action movies, I can tell you that lots of movies in this genre from the 60s/70s, even some of the 80s have more depth (due to better screenplays) than most of today's. In my opinion, at least. These were the last decades action movies were called thrillers, then priorities changed...
Some recommendations: Bullitt, The Getaway, Point Blank, Assault On Precinct 13, Bring Me the Head of Alfredo Garcia, Marathon Man, The Parallax View, All The President’s Men, Three Days of the Condor, The French Connection I & II (both are excellent), Charley Varrick... the list of great, more realistic Hollywood thrillers/action movies could go on forever and then there's this once great movie nation called France (Le Clan des Siciliens/The Siciiian Clan, Le Cercle rouge/The Red Circle, Le Samouraï/The Samourai, A Bout de Souffle/Breathless...).
A special recommendation from the 80s: William Friedkin's brilliant, dark cop thriller "To Live and Die in L.A." from 1985 starring young William "CSI" Peterson and Willem Dafoe. It's a Hollywood movie, by the way. 
These were just some great, more realistic movies from the action/thriller/crime drama genre. If you want, you'll find hundreds of more realistic, deeper movies in all genres, from both, inside and outside Hollywood.
