I think the real meaning of "vine-ripened" in produce-department advertising lingo is "not picked when still dead green and rock hard".
Things that you allow to get mostly (or even, frankly, *partly*) ripe on the plant will aways be waaaaay better than ones picked when they're like small green bowling balls.
However that is not of any real relevance to home gardeners
Personally, I like a tomato with a bit of texture and tang to it, and I find that many varieties just get a little too mushy and bland if allowed to get 100% ripe on the vine. So I often pick 'em when they are only about 98-99% ripe, and let them sit in the kitchen for a day.This is totally a matter of personal taste however.
There are some things that should NOT be allowed to ripen on the plant. Bartlett pears come to mind. Ripened on the tree, they are gritty and stony. Picked when ripeNING but still firm and a bit greenish, and ripened in a cool kitchen or pantry, they get all buttery smooth and juicy and the way a Bartlett type pear should be.
Then there are other things, like cantaloupes, that stop dead in their tracks the moment you pull them off the vine, so they'd better be dead ripe when you do it.
Pat