The best rpg games like Legend of Dragoon are Legend of Legaia, Shadow Hearts: Covenant and Final Fantasy VIII. Below are 9, 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 Legend of Dragoon 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.
The other PS1 RPG built on input combos rather than menu picks.
The Judgement Ring makes every action a timing check — the closest system match.
Timed triggers on attacks and summons, same generation.
A modern turn-based RPG where timing every hit is the whole combat system.
The best-paced JRPG of that era, with combo attacks between characters.
PS1 RPG with combo inputs and a far more ambitious story.
Timed chain attacks and a very unusual combat system.
The spiritual successor to the PS1-era Final Fantasy feel, with a timing ring.
The best action-timeline battle system of the generation.
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.
The full list is on games like Legend of Dragoon — 9 picks, no genre filter.
Legend of Legaia. The other PS1 RPG built on input combos rather than menu picks.
No. Legend of Dragoon 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 Legend of Dragoon 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.