Unfortunately it isn't possible to pull up DVR recorded programs (or really control DVRs) with either GTV or the XBox One without using the DVR's remote. So in that regard, neither the Channel Master, HomeWorx, or Tivo will probably perform similarly. You should be able to pause/play/rewind/ff live TV, but not much beyond that (without the DVR remote).
One other comment...for me as a cordcutter, the XBox One performs far better than the GTV ever did. I control nearly everything with voice commands; it's not a gimmick--it works very very well. Unlike my GTV, the channel guide works flawlessly. Not only does it pull up a guide for OTA, it then let's me create my own customized guide of "favorites." This allows me to basically weed-out a ton of channels (mostly shopping & religious) from my guide. And you can just say the name of the show or channel you want to watch and it'll jump to it. I can also just say "pause" during live TV and it'll do so via my HomeWorx DVR..foice commands of "play," "rewind," fast forward," and "faster" work too. To schedule a recording, however, I still need to grab the HomeWorx remote--but that would be true whether you were using any DVR (including a cable TV box).