This is exactly what I was thinking about -- why the contemporary art house cinema is chock-a-block with Antonioni's heirs while Bergman's are nowhere to be seen.
"Today, we are aswarm with Antonioni imitators, but no one seems to want to be the new Bergman," Michael Atkinson notes. That's partly because nobody can be the new Bergman. And not just for the obvious reason.
Unlike a lot of younger filmmakers today, Bergman was a highly, richly cultured individual. He knew the Bible backward and forward, Shakespeare too; fine art, music, and so on. All of his knowledge did more than inform his work—his work is suffused with it, it gains much of its texture and heft from it. Of course, Antonioni is similarly cultured, but his depth in this area doesn't play so much upon the surface of his work; it motivates the form, rather than thickens it. Today's young filmmakers aren't, for the most part, as polyglot. For a lot of them, all the culture they've got is film. And Antonioni's got a signature style that's accessible to them, and seems imitable: shoot some architecture and negative space, have characters disaffectedly utter banalities, and you think you've got it. To emulate Bergman, you've got to know what he knew, and knowing that...go on to be yourself.
That's one reason certainly but I think it is also because over the last couple of decades the focus has shifted from Europe, and as a result from the European high culture, to everywhere around the world. Europe no longer has a monopoly when it comes to serious cinema.
There is also the fact that the themes of urban alienation which Antonioni made his own are so readily applicable to rapidly developing Asian cities. One of the reasons why we have so many Antonioni imitators in Asia.
Tsai Ming-Liang is perhaps the most talented of the young Asian filmmakers whose style can also be compared to that of Antonioni. (Bela Tarr and Michael Haneke too.) I wanted to link again to my favourite crying scene in the movies ever but the youtube guys have deleted the video. If you haven't seen it you have to do with the description there. It is a typical Antonioni shot. Long unbroken tracking shot, a non-subjective moving camera following the girl as she walks in the park. Only after a while you will realize that it is not just the girl the camera is tracking but the park. The desolate park in fact is much more important. She doesn't have to speak anything. There is already a visual correlative to her inner life all over the screen. These types of shots are all over in Antonioni's films.
Some older posts about Antonioni with links here.