Basically a lifestyle choice - all about how you want to interface with your music.
The SB has to get the files from somewhere - there is no way to rip directly into Squeezebox... so you rip into iTunes and access the library through the SB browser, or you rip to something else (FLAC if you are a PC person) and do the same.
This is a classic Mac versus PC thing - Mac is Apple Lossless. PC is EAC to FLAC. You are pretty much stuck with the OS. The big difference here is that the SB will do FLAC...
Apple TV can be linked to your master library and/or you can download any combination of media up to the capacity of the ATV you purchase. Personally I replaced an SB3 with an ATV preferring the HDMI link to my pre-pro in my HT rig, but that was more about engineering then sound quality.
Please note that the ATV itself has no impact on sound quality. It is a question of what you connect it to.
In comparison, the SB offers the choice of using the built-in analog or feeding SPDIF to an external DAC.
I found that by the time Wayne at Bolder gets done with a power supply upgrade and an analog upgrade you have a wonderful source for much less then most name DACs. On the other hand if you already have a DAC you are happy with and it has an available input, that could tip the scales and would certainly save you the mod cost.
Obviously both the SB and the ATV can be connected via Ethernet or WiFi so that's a push.
I would have to give the SB a slight edge if your goal is a multi-room setup with each room being able to access its own music.
You can navigate the ATV with an iPhone or iTouch, or simply do it on screen if you are set up that way. There are various PDAs that can be combined with 3rd party software to navigate the SB browser. There is no way that I know of (which don't mean jack) to put the SB browser on anything but a computer display.
If you are also an iPod user, I think that it makes sense to keep it all in the Apple family.
Hope this is somewhat helpful. As I said at the top,this is a lot more about how you are going to use it and what else you have going on.