As long as the folks involved are reasonable, one DM could run LBB OD&D and another could run Path(math)finder WITH THE SAME CHARACTERS and general setting.
Hell, you could even throw Runequest, Tunnels and Trolls and a ton others in the mix.
Plus using different rulesets provides a DM a rationale for abruptly shooting down "But last week when Monty was DM I could do that!" whinging; "Different ruleset bub, deal with it!"
Just a picture of a pit bull (ish?) on a treadmill being cute; has nothing to do with this post.