Replay gives you much more control over what you record. The Replay Zone feature, where you record shows based on keywords, is pretty powerful. Post comments, rants, and raves on the Fresh Gear Message Board . TiVo is more of a black box. It's much easier to use, but you don't have nearly as much control.
Replay is much more powerful, but requires more care and feeding.
If you have cable today, TiVo is the right choice. DBS Satellite customers who also want to see local broadcasts should opt for Replay. But that's today. DirecTV, the largest DBS satellite vendor, just invested in TiVo. In addition, TiVo promises a multi-input option soon.