As an owner of three different series of TiVo and a frequent viewer and participant of the TiVo Community forums, I can tell you that TiVo and its latest Hydra is just as controversial with a lot of haters and some likers. And let's also add that DirecTV's latest UI update is also just as controversial as tivo's Hydra and Hoppers carbon UI with a lot of haters there DirecTV as well. It is so unfortunate that dish DirecTV and TiVo are all in the same quicksand when it comes to the latest DVR's they offer. No it really isn't greener on the other side of the fence at the DirecTV or TiVo. Unfortunately the new TiVo VOX will by default come with a hydra with no option to go back to the older UI unlike older TiVo DVRs that had Series 5 UI can revert from Hydra if they can't stand Hydra but of course they lose all their recordings in the process. Put simply, Genie, Hopper, TiVo and Hydra are all a mess right now. And even uses of Hydra are now complaining that some of their recordings have not been made that their one passes are not working or that recordings some have been erased before they had a chance to watch it. Okay, it seems like dish and TiVo have much more in common they what your idea of trades suggest. And there have been some people who left TiVo specifically because of Hydra and the rovi metadata mess before it and a few other rotten changes before that too. Meanwhile the older TiVo S3 S4 and S5 work very well not so for Hydra. That's a lot like the older dish VIP DVR that seem to be working better than the new carbon you are DVRs.
For what it's worth, dish echostar already has lifetime license of all TiVo patents--pre-Rovi acquisition-- as part of the old Tom Rogers TiVo patent settlement. Dish also has more recently licensed some Rovi patents that it is using as well. And of course dish, among the other largest and MVPD's, had dumped Gracenote and now have agreements to use the Rovi/TiVo metadata, and that was a a degrade and we're still waiting for Rovi to clean up its mess ever so slowly.
To answer your question OP: no , we're not interested in trading infuriating dish problems for infuriating TiVo problems, nor are we interested in trading in for infuriating DirecTV Genie problems.