I have no experience with the Cowon Z2, so I can't speak to any advantage it may have. The review I read on this forum was only personal opinion, no actual tests. It may be just fine. MP3 present very little challenge to any player, should be the easiest to deal with. At the price though, I'd definitely get an iPod.
A player has just a few things to do. It has to store all the music you want, have good audio quality, and be easy to deal with operationally, including sync with your library. iPods do all of those things well, and more. The Cowon has quite a good feature set, but I have found no company as focussed on the user experience as Apple. They do know what it takes to make an easy to use device. It's also nice, if you live hear a larger city, to walk into an Apple store and buy your player, or accessories, or talk to somebody if you have a problem. I don't know of any Cowon stores.
iPods have excellent amps in them that are quite capable of driving many headphones. There may be a small advantage to have a good amp with an iPod, but only when used with certain headphones. I'd try the iPod with no amp first, then study the impedance curve of the headphones you want to use. If it's every low, or swings up and down a lot, an amp may be a good choice. If the headphones need a lot of drive voltage, an amp helps too.