For all the "Why not port the PS3 remaster?" questions: this method was likely easier. Sony has a working PS2 emulator for the PS4. Outside of maybe having to account for the technical weirdness that the original J&D did, getting them running on that emulator was likely a simple process. Porting the PS3 builds would be significantly more work, probably more money than they're willing to spend on J&D right now.
As for how they'll run, generally the PS2 on PS4 games run as well as they did on the PS2, and occasionally a bit better (Okage has much better load times on the PS4, for instance). Outside of the occasional new bug (Hi Wild Arms 3!), I wouldn't worry. If you can stand to play the PS2 original, this one will be fine. I'm not familiar with how well the PS3 remaster worked so I can't say if it's better or worse.
Seeing J&D in this service is a good thing, because it means we're likely to see other series that had PS3 remasters (Ratchet, Sly, Ico/SoTC, etc) make it to the PS4.