Premiere 4 and Premiere 4 XL (I think that's what it's called, the main difference is hard drive size), record 4 channels at once.
Yes, they work as well as your DirecTivo.. Better, since you can download (non protected) shows to a computer, or use with a Tivo Stream, etc.
Tivos have some ads, but they are MUCH less intrusive than what I've ever seen on cable boxes.
I hate ads, and wish I could pay EXTRA for no ads, but again, Tivo's level of ads is FAR less objectionable than others, even though they're "all over the place".. They're in inconspicuous places in most cases.