Aaaaaand there goes my night. Very interesting site!
Consulting Cinemetrics (a wonderful site) it turns out that the franchise under Berman actually had less cutting than it did in the '60s.
(Just do a search for "Star Trek," sort the list by average shot length, and you'll see what I mean).
The information is user-provided, so it's not a perfect tool (you can see multiple entries for TWOK with varying ASLs, for example), but it's still a useful one.
What strikes me as interesting is that Star Trek Into Darkness has longer shots than its predecessor.