Let me see if I can make sense as I explain this....
I have DirecTV (satellite) for my expanded stations, but rely on Cox Cable for my Basic/local stations. Since I have only one DirecTV receiver, whatever I watch on the "living room" television on satellite is what is seen on all the televisions in my apartment. The only way to change the channel is to physically change it on the living room television. Thus, the ReplayTV has to be hooked up to that television in order to record any shows that I am interested in.
I have not been able to figure out how to watch basic cable and record something on DirecTV since they are on two different sources. (In order for me to tune in my basic/local stations, I would require a new satellite dish and an additional receiver for my bedroom. Meaning more $$$, which as a college student I can't afford right now.) I also need an RF modulator for my TV since it is OLD and outdated.
As for my dad and his TiVO...he records EVERYTHING!! He is a History channel buff, plus he recorded the entire Tour de France. Until recently he and my mom lived in two separate houses that required them to commute on the weekends to see each other. *YUCK!!!* So, he just set it to record, and could watch "his" shows when he got home. Not only did he record the previous mentioned shows, but he recorded Sopranos, Track and Field meets. He loves it!!!! I loved mine also. Just haven't worked out some bugs yet since I have the minor problems in my apartment. It is great.
ReplayTV has the advantage of being able to share recorded shows over the internet if you missed a recording, something you can't do with TiVO. I found this website when I was such a hard time with ReplayTV's customer service...Check it out:
AVS Forum: ReplayTV Forum
They were great for answering any questions that I had about my ReplayTV. In fact one person took it upon himself to help me get my ReplayTV hooked up when my father gave up!!
Hope I helped some...sorry about the length...