The $200 Roamio will record 4 shows at once (same as my Mac mini setup). It can also hook up to optional equipment like Mini to watch live and recorded TV in other rooms as well as Stream for watching TV on your mobile device from anywhere you have internet access.
The $150 $75 (appears to be on sale) Premiere will record 2 shows at once and will also work with Stream.
Both require a $15 monthly subscription or $129 annual subscription. Both record up to 75 hours of HD content, and can be expand with an external drive.
The AirBox I blogged about last week doesn't specify number of tuners - if it's just 1 then a TiVo might be a better option, even with the slightly higher monthly cost. Also the TiVo will work in cities that don't have AirBox (I suspect these are the only markets that Airbox is available in).