It's not 1080p. Most PS2 Classics render at 896p on PS4, I believe.
IMO, it's fine for me so far. Really, I think it's the best (official) release so far, simply by virtue of being at a much higher resolution than the original PS2 version (which looks horrid on an HDTV), and allowing you to play it in it's proper 4:3 aspect ratio. The "HD" Collection (which wasn't actually even in HD) forced you to play it in the "wide-screen" mode, which was terrible, and basically the same 16:9 implementation as seen on the original PS2 version (it basically just cropped off half the screen, and was the equivalent of zooming in the picture with your TV). Also, it runs reasonably well for me on PS4 PRO with Boost Mode enabled, at least. Only a few minor dips here and there.