I live in an association that provides cable + internet for a bulk rate (it's super cheap). With that, I get 3 free boxes, and a free cable modem. So at least for me, the DVR service won't change. That said, even if the DVR service is identical in price to Tivo, I don't have the up-front cost of buying the box, and when the equipment gets older, I can just swap it out (since it's a lease).
I have had both the "old" motorola boxes in the past, as well as the X1 box (no DVR). IMO, each solution has trade-offs. The power user features are really nice with Tivo, the ability to move shows to PC is really awesome, and the ability to upgrade Hard Drives is great too (have done this twice, even when it was harder). Overall, I did PREFER the Tivo, but it was only slightly, over the X1 boxes. For me, ads tip the scales just enough. I will keep my Tivo, I will opt out of ads, but I will NOT give Tivo another dime until the practice stops. If they reverse course, great. If not, when this Tivo dies, I'll get an X1 box and see if I can tolerate it. If not, I may try Channels. At this point, both are slightly cheaper overall (and Channels would give me an excuse to get a NAS, just have to see if TV Everywhere works enough for me during the trial first).
To me personally, TE4 and X1 are pretty similar UI's. I have a harder time seeing, so the X1 wins out slightly (although I get around this by using the app when I need to see the guide) in that regard. As I stated above, remote play, watching on PC's, tablets, etc. and playing on secondary boxes is more stable on X1, but the Tivo UI is slightly faster (until the ads start, I don't need yet another chance to see a BSC). Voice on X1 is a killer feature (but I am sure it's great with VOX too).