To me it almost feels like two different moves, based on some variable combination of situational necessity and/or the player’s comfort level with that particular machine.
You’ll see many highly-skilled players do the “quick flip” drop catch in situations where the decision has to be made instantly. In those situations, the “hold and release” isn’t even possible.
This is a lot easier to achieve when you’ve played the game enough that you have a good feel for speed/flipper travel on that game. Your brain knows where the flipper is going to be when up, and how long it takes it to get there, and come back down upon release.
In some situations, when the movement of the ball is mostly horizontal toward the flipper, the “quick flip” is required to get the tip of the flipper out of the way of the path of the ball.
You might also be able to apply the same logic that theoretically, live catches are assisted by the fact that at the end of a flip, the flipper travels just a tiny bit past it’s up-resting position before settling. This can dampen the speed of the ball before it the flipper is pushed firmly down into it’s up-rest position.
You might have observed extreme versions of this on flippers with worn-out mechs, where you can just hold the flipper up and it will sort of auto-live catch.
On a quick flip drop catch, which Werdrick definitely uses more frequently and consistently than anyone I’ve observed, it seems possible that the same “give” assisting a live catch could also assist a quick flip drop catch done at the last possible moment.
Aside from that, sometimes it just seems to be more related that player’s rhythm with the machine, and not really a conscious decision at all. I’ve personally never considered them to be different enough to classify separately. I view the “quick flip” drop catch as just a more nuanced version of the “hold and release”. I’ve definitely observed it happen in my own play, often unconsciously, and without any applicable rhyme or reason for that particular instance.
I’ve also observed myself accidentally drop-catching directly into the drain more often than I’d like to admit, which I do not recommend unless you are in a situation where you need the ball in the trough ASAP. It is kind of interesting that the drop-catch-to-drain seems so easy to do on purpose, even though the timing is so close to that of a proper drop catch.
TL;DR It depends