From what I remember hearing about FF1 PSP it is another DoSish style thing with yet again very minor tweaks here and there like most of the ports. It isn't say FF3 level. I presume FF2 is roughly the same just off hand.
To be specific...
Both games have redone graphics cause OMG THIS MATTERS SO MUCH, etc. They're still 2D. Also uses the Origins version of Music, which is the same as DoS but better quality, etc.
FF1 sounds like it just adds in boss themes for the SoC bosses (eg Battle on the Big Bridge plays for Gilgamesh instead of the Fiend Battle theme, the other bosses get a remixed version of bosses from the home game), and a grand total of ONE MORE AFTER GAME DUNGEON complete with a few new equips (cause apparently the SoC equips weren't cracked out enough, with some obsoleting freaking Masamune).
FF2 adds in apparently like 4 new dungeons or something called Arcane Labyrinth, complete with 2 new spells and a unique equip for every PC in the game.
Yeah, they're basically just another "enhanced port" thing and not really a remake.