It only matters to me on a technical standpoint:
Audio track (e.g., Close Encounters of the Third Kind 30th Anniversary Ultimate Edition R3, DTS same as R1. Jaws: 30th Anniversary Edition R1, DTS -- R3 doesn't have DTS track.)
PQ/SQ/format (e.g., The Last Emperor Criterion Collection [R1] 2:1 vs. The Last Emperor [R3 Hong Kong release] 1.33:1)
and
Special features/packaging (e.g., The Poseidon Adventure [1972] 2-Disc R1 is exactly the same with the R3 version. The difference is, R1 has Lobby Cards included.)
I'm not much of a special features person, only when the movie is really interesting on many technical aspects (as with the
LOTR Extended Edition trilogy) that I dive into what the director and crew have to say. Else, it kills the magic for me. Many R3 Warner releases are no-brainers since they more or less contain the exact PQ/SQ and Special Features as their R1 counterparts -- with a few exceptions.
Batman Begins R3 doesn't have the MTV Movie Awards spoof feature. Not really a big deal, in my opinion. Also, I heard that
Blade Runner: the Final Cut R3 doesn't have the preview trailers of other warner releases that the R1 has. I'll have to check my two copies later to confirm (I bought the R3 because I just couldn't wait for my R1 5-disc Ultimate Edition gift set to arrive and I really wanted to see Sir Ridley Scott's changes already!). Other than minor commercial changes, both releases of Blade Runner have exactly the same special features and PQ/SQ, to my knowledge.
Since a lot of R3's are of good quality naman, that's the bulk of the movies I get. Yun lang