The Snowball is intended for home studio recording, meaning it is intended to be plugged into your computer so you can record and edit audio files in Digital Audio Workstation software such as Audacity or Logic--the Zoom is a stand alone recording device which creates audio files and basically contains it's own(very limited) DAW. Basically, the Snowball plugged in to a computer and the Zoom are different recording options, one portable, one not.

You can actually plug the Zoom into your computer to use the microphones only, and you definitely can upload the audio files to your computer to edit in your DAW--but the Snowball, which is made by Blue(who make professional studio mikes) will give you much better sound quality. It's become kind of a standard for home audio recording for this reason.(and it comes with a mike stand and can be mounted on a boom, which is really important).

A handheld recorder is really handy to have for everything from recording live sessions to saving ideas, but if you want to do multitrack stuff, it is so much easier to work on computer.

And Joe--a USB mike will be much superior to an analog plugged into "good" computer sound card--you'd need a professional soundcard to get a comparable sound--