This is one of my favorite games of the late PS2/Xbox/GameCube era, people tend to bring up "Red Dead Redemption", or it's previous game during that era "Red Dead Revolver", but I sadly don't see many mention this game at all. Was developed by Neversoft, which I miss for the first 3D Spider-Man game they made, and their Tony Hawk games especially. To go from Tony Hawk, to a more than capable 3rd person open world western, it's beyond impressive. The world itself isn't actually that big, but it helps that it's not overly big either, making it fun to traverse and complete all the side-quests.
I also greatly enjoyed the acting from all the major actors hired for the game, the story itself is also a fantastic time, the music adds to the overall vibe immensely, the graphics are also impressive for their time, there's plenty of side-quests to lengthen the whole experience, and I've enjoyed playing this title multiple times over the years, not once have I second-guessed replaying it, and now I've even played the PSP release!
PSP shouldn't be the first platform you'd play it on, but it's beyond impressive how they pulled it off, with extra content. I'd always recommend this game, on any of the previous platforms I've listed, to Xbox 360, or even PC, this is always worth the purchase!