There's plenty of games that have come out for both PS3 and PS4, usually some time apart.
South Park: The Stick of Truth is the most recent example, and the one I'm most keen on checking. I've got a fair amount of progress in the game on the PS3, and since there's a free copy on The Fractured But Whole, it'd be nice to keep playing, but on the PS4.
Trying to double-check if there's a way to transfer/convert the save game data to the PS4 version so I can keep playing there. I don't think there's any transferable bonus between the game, as there are in other series, so that's not an issue. just trying to avoid having the switch between consoles.
There's any other number of games I wouldn't mind doing that to, if it were possible. Skyrim is a good example. I found a program to convert my PS4 save to PC, and that was useful.
There may not be an across the board answer on this, and it looks like games that are set up for server communication, like Destiny, have such functionality, but I'm curious if there's a go-to solution, or if it's more a case by case basis, or if it's just not a thing for non-server/cloud based games.
(Very likely a duplicate question, but couldn't find one that hit the topic precisely.)