Thexder Neo preserves the gameplay of the original: your ship can either fly through maze-like 2D levels, or it can transform into a walking robot at the touch of a button and navigate the levels platform-style. The ship is faster, but the robot form has multidirectional fire, which is important, because you are swarmed at all times by annoying little enemy ships. Success in Thexder requires frequent transformation back and forth, using the fast flight mode to advance through the levels, and then dropping into robot mode to clear the screen of enemies. It also requires more skill than I have. The skill isn't as strategic as Bangai-O (another free-scrolling shooter), where you have to choose from multiple weapons and methodically eliminate hundreds of threats as you carefully progress -- it's more of the traditional "shoot everything really quickly" type of game.
The PSP's most important contribution to Thexder isn't the new 3D graphics, although they are delightful. The real benefit to having this game on modern hardware is that previous versions of Thexder were rather jerky in motion, but Thexder Neo runs at an appropriately smooth framerate for a shmup.This is the kind of remake I can approve of: it uses powerful hardware to make the already great mechanics of a classic game work better, and, as far as I can tell, doesn't mess with the game otherwise.