The best rpg games like Parasite Eve are Vagrant Story, The 3rd Birthday and Koudelka. Below are 5, each with the reason it is here — and, at the end, what filtering to rpg costs you.
Filtering to RPG means you want progression — a character to build or a party to grow — layered on top of whatever else you liked.
What you get: A reason to keep going after the novelty wears off. RPGs are the genre that reliably converts hours into feeling more capable.
What made Parasite Eve worth playing in the first place is covered on the full list. This page is the rpg part of that answer, and only the rpg part.
Same era, same Square ambition — deep weapon crafting and a hostile city.
The direct sequel, third-person shooter rather than RPG.
Horror RPG on PS1 with grid combat and a genuinely grim story.
Koudelka's spiritual successor — horror RPG with the Judgement Ring timing system.
Modern city, psychic powers, body horror aesthetics, action-RPG combat.
Immediacy. Almost every RPG asks for a slow first few hours, and the systems that make hour forty good are the same ones that make hour one a menu.
Specifically, these are strong answers for Parasite Eve that are not rpg games, so they are not on this page:
The full list is on games like Parasite Eve — 9 picks, no genre filter.
Vagrant Story. Same era, same Square ambition — deep weapon crafting and a hostile city.
No. Parasite Eve released on the PlayStation, but a recommendation is only useful if you can play it, so the picks above span platforms and eras. What they share is the genre and the reason.
Whether the stats are the point. In an RPG the build decides what you can do; in an action game with stats the build only decides how fast you do it.
No. The picks below span turn-based, real-time and action RPGs, and each one says which it is.
By hand. Each pick was written for the full Parasite Eve list first, on what the game actually does, and this page is the part of that list that is rpg — never a genre tag lookup, which is how "best racing games like Super Mario 64" used to be a page on this site.
Or read the rpg guide for where to start in the genre generally.