They are such different devices I dont think you can really compare them. The Apple tv has video, built in HDD, can connect to the internet, etc. The squeeze box just plays music from your computer.
If you just want something for music I personally think the Squeezebox would be a better way to go because number one it doesnt have a HDD which inevitably will fail. The couple of Apple tv's I installed got so hot I cant imagine they will last very long, I really could not believe how hot they got. They are pretty slick though and I wouldnt mind having one if i wanted to pay $300 bucks for something that probably wouldnt last 5 years.