In short - it would probably look and feel a lot different. Raiders, although not a cheap movie, had quite a tight budget and if it were made today, would probably require quite a bit of CGI to meet the production requirements e.g. virtual sets etc. etc. It would probably look much more like KOTCS than it would the original Raiders. That of course doesn't mean in has to be as light in tone...
As far as Montana's reference to Batman Begins and TDK is concerned. I think it's like comparing apples and oranges. BB's & TDK's strengths (IMHO) are based around mood, dialogue and character. The set pieces are largely secondary to the more important stuff contained elsewhere (which is fair enough). Indiana Jones is very much about the big sets, huge set pieces and well constructed/conceived action sequences.
I thought the truck flip in TDK was great, but it was (for me anyway) just 30 seconds in an otherwise boring, uninspired and very predictable chase sequence. Again - not a problem for me as TDK's strengths lie elsewhere. And if you look at the biggest set piece of BB (the monorail bit) it's largely CGI too. I personally thought the action/set pieces in KOTCS - the warehouse, Doom Town, the jungle etc. etc. were infinitely more imaginative and exciting. Saying that, neither the action in TDK or KOTCS comes close to the truck chase, the rope bridge or tank chase from the previous Indy movies. So I don't think it's as black and white as one technology over the other (although I think we'd all agree that the more live action the better), but it's more about what's driving the action on screen... and does it serve a purpose.