Pokérole is also a pretty good system to run a Pokémon Tabletop RPG with. It relies on a simplified system based on dice pools that still manages to approximate the experience of playing the games fairly closely without getting overly crunchy.
Yep, no trainer classes. It's much more barebones on the trainer side. The diferentiation between them is largely based on what skills they specialize in and what sort of teams they have. I've used it in the games I ran because it was much faster and easy to handle compared to all the stats and bonuses that PTU has, while still feeling like Pokémon. PTU definitely has a lot more options, but it's a lot more work to run.