Three types of iPod right now: shuffle, nano and the video iPod
video iPod: most storage, but also largest. can play videos too. hard drive.
nano: a lot smaller than video iPod, but can't do video. doesn't store as much either. flash memory.
shuffle: no screen or clickwheel, just put your songs on and play them. very small though, easy to use. flash memory. not a lot of space either, less than nano. same as your current one though.
flash memory means storing things on microchips that don't move about when you move about. the hard drive in the original iPod has little moving parts in it. while all three won't skip much if you do any jogging and things of that nature, the nano and shuffe definitely won't.
should you keep current mp3 player or get an iPod (any of the above)? Up to you. what makes them different is what makes Apple computers different from other desktop PCs with windows on them: Apple. They make things that integrate very well, and have great interfaces on them. For browsing lots of files, you can't beat the clickwheel system. Others try to copy the iPod to get in on the money they're making, and end up almost copying the iPod outright. Managing the music on your iPod and your computer is very easy with iTunes (it all integrates together, making stuff easy).
Short answer: if you're happy with your current mp3 player, stick with it. If you get annoyed with things about it, tell us them here, and maybe we can tell you if having an iPod would solve any of your annoyances.