The best rpg games like Dragon Warrior Monsters are Dragon Quest Monsters: The Dark Prince, Pokemon Emerald and Siralim Ultimate. 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 Dragon Warrior Monsters 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 modern entry, and the breeding system is intact.
The generation with the Battle Frontier, if you want the other approach.
Creature fusion taken to absurd depth, and effectively endless.
Collecting plus a team-building puzzle with real strategy.
The best non-Pokemon monster collector, with a clever type system.
The other great non-Pokemon collector, and the raising is the game.
Straightforward, funny, and full of creatures to catch.
Creature collecting with real depth in the battles.
A faithful classic-style monster RPG with modern quality of life.
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 Dragon Warrior Monsters — 9 picks, no genre filter.
Dragon Quest Monsters: The Dark Prince. The modern entry, and the breeding system is intact.
No. Dragon Warrior Monsters released on the Nintendo Game Boy, 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 Dragon Warrior Monsters 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.