I DL'd pretty much every RE game available on PSN the other day... but progressing through them slowly.
They are certainly not HD haha... but you have some options for "smoothing" which imo is a mixed bag, results vary by game. It's better for some PS1 games, worse for others.
I'm playing on the Vita which offers a couple more options... but overall the games are still kinda gross looking. Sorry, it's true.
What I've been doing with RE1

C is playing through a section, and then watching the same section from REmake on Youtube haha...
Anyway, from what I played of RE1 it looks better on Vita than on my Monitor/PS3.