The lights are on
I know I'll be hanging on to my PS3 for most of the reasons already listed and for this reason. Completely hypothetical situation (though not impossible), let's take Assassin's Creed IV for example. Let's say on launch day, the PS4 version (despite the so-called "developer-friendly feel" it has) plays a lot like Assassin's Creed 3 did for most consoles: unresponsive at times, frame-rate loss, etc). Yet the PS3 copy plays rather well because developers have figured the console out. Like I said, it's hypothetical, but there is that looming possibilities that these launch titles won't be up to par just yet.
I'm just guessing here, but I'd like to think it works just like how the Vita syncs to your trophy list. If you have both the PS3 and Vita, your trophy library shows a combined list of the games you've played with trophy support. The Vita games (or versions) will be distinguished by a rectangle with the word Vita under it to let you know you've earned it the other console. Having said that, I'd like to believe the PS4 will work the same way with your profile, especially given how much emphasis Sony put on trying to link the Vita to the PS4. As RxWhitePony stated, your PSN profile will have you covered.