The Zune concentrates on being a Portable Media Player. Not a web browser. Not a game machine. Maybe in the future it'll do even better in those areas, but for now it's a fantastic way to organize and listen to your music and videos, and is without peer in that regard. The iPod's strengths are its web browsing and apps. If those sound more compelling, perhaps it is your best choice.
If you're still on the fence: grab your favorite earphones, head down to a Best Buy and ask to plug them into a Zune then an iPod and see which one sounds better to you, and which interface makes you smile more. Then you'll know which is right for you.
Hands down, Apple's app store wins by a mile. It's a huge selection of all sorts of apps vs a rather sad selection of a handful for Zune. Microsoft has plans, especially in the realm of games, but I'm not sure I'd want to bet on the future if this aspect is important to you. The iPod is a much better choice in that case.
Zune and iPod: Most people compare the Zune to the Touch, but after seeing how slim and surprisingly small and light it is, I consider it to be a rather unique hybrid that combines qualities of both the Touch and the Nano. It's very colorful and lovely OLED screen is slightly smaller than the touch screen, but the player itself feels quite a bit smaller and lighter. It weighs about 2/3 as much, and is noticeably smaller in width and height, while being just a hair thicker.
Apple now has Rhapsody as an app, which is a great start, but it is currently hampered by the inability to store locally on your iPod, and has a dismal 64kbps bit rate. If this changes, then it will somewhat negate this advantage for the Zune, but the 10 songs per month will still be a big plus in Zune Pass' favor.
This is getting a bit more subjective, but I much prefer the Zune Marketplace. The interface is colorful, has more flair, and some cool features like 'Mixview' that let you quickly see related albums, songs, or other users related to what you're listening to. Clicking on one of those will center on that item, and another set of "neighbors" will come into view, allowing you to navigate around exploring by similar artists, songs, or users. Speaking of users, the Zune "Social" is also great fun, letting you find others with shared tastes and becoming friends with them. You then can listen to a playlist created based on an amalgamation of what all your friends are listening to, which is also enjoyable. Those concerned with privacy will be relieved to know you can prevent the public from seeing your personal listening habits if you so choose.