I'll gear this review to 2 types of people: current Zune owners who are considering an upgrade, and people trying to decide between a Zune and an iPod. (There are other players worth considering out there, like the Sony Walkman X, but I hope this gives you enough info to make an informed decision of the Zune vs players other than the iPod line as well.)
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.
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.
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.