I have only two early Criterion DVDs--Robocop and Time Bandits--but there's no way I'd get rid of either, despite that they no longer look so good on a 16:9 screen. I mostly hold onto them for the extras, which later versions don't have.
As far as replacing DVDs with corresponding Blu-ray versions of the same titles, particularly collectors' sets: Depending on what extras or premiums from those DVDs are included in the Blu-ray version, I won't likely get rid of the DVD if I see no real reason to. I have the Ultimate Matrix Collection on Blu-ray, but I also have the limited edition DVD set with the Neo mini-bust and the expanded booklet, as one example; another are the Star Wars original trilogy box and the prequel singles I still have, in addition to the Complete Saga Blu-ray set, just because of the extras. I'm somewhat a completist, so I don't get rid of anything if there's something that might be of value.