Funny enough, as you can tell from my signature, I no longer have either of those tables.
I have the first version AppleTV with an upgraded 160GB internal hard drive. It's synched to a media server I host in the house. Leaving iTunes open on the server, I can stream anything to the apple tv. I used it mainly for music. I don't notice a difference between what fits on the drive space and what is streamed ( I have 500GB+ music). It appears to be the same quality. I use the optical out into a DAC and notice a large improvement as compared to using the regular RCA outs. I have an app on my ipod touch that I use as a remote so I do not have to use my tv to view my audio menu, i can just select songs on the ipod touch and play. Iphones have the same app.
I also use it for video as well, running a hdmi cable to my tv. On the newer AppleTV's, you don't have a drive but you can stream/view your desktop which the older versions cannot.
I don't have any experience with a Squeezebox or other devices but i'm sure others on the forum can comment on their functionality.