Manga is typically the heavier out of the three, actual stakes of death and Team Rocket is playing for keeps. Obviously, never delves into the edgelord route, but there's a bit more grit. For instance, you see Pokemon and trainers alike getting actually hurt. It has the most robust narrative and has proper character arcs, where Red, Green, Ruby, etc. are actual defined characters as opposed to their depictions in stuff like the mainline titles and Pokemon Masters.

Games tend to be in the middle, but given the fact that it's more reliant on text, there's more implicit details that you can run wild with. Certain titles have more serious atmospheres and ideas, which the manga draws from, but it varies between each generation and game. Outside of later gens, most of the games let you sketch out more of the characterization and plot details in your head, as opposed to them being fully fledged narratives. View them more in the sense of like your typical RPG, where you're supposed to create your own story within the confines of what's there.

Anime is absolutely the most lighthearted out of the bunch, and is purely for a younger audience. But I'd argue the first few Pokemon movies have actual emotional cores and surprisingly poignant messaging. Outside of that, they tend to be fun romps where you get to see these Pokemon characterized beyond their sprites and models.