Since I just switched here is the obvious advantages and disadvantages on the 2 dvr's that I noticed. This is late 2017 I'm answering so if someone is reading this years later it may be updated.
1) Direct tv allows 5 channels to be recorded at the same time, Dish hopper only allows 3. This is a big deal, you would be surprised how often you hit the 3 limit, especially because there are times overlapping shows hit this all the time. 5 is much better.
2) Direct tv dvr allows you to jump back and forth with 2 currently recording shows and "resume" where you left on on each. Dish hopper does NOT do this, you have to start over at beginning. This is a really big flaw with hopper, because when recording 2 sports shows you often jump back and forth as you catch up watching on each, and as you skip over the in between stuff you catch up and want to resume where you left off everytime you switch back and forth.
3) Dish hopper has a much faster plus 30 second jump button. When you use the 30 jump button on direct tv it foward through it, on dish hopper its instant. Much better on the hopper dvr for this.
4) The menu on dish hopper is better when you record items as it marks shows that are not recording but are currently set to record new episodes. It just marks this much better on the hopper menu.
5) Hopper is better for recording sports teams, because I can say "record all new games with team X". On direct tv you can lookup favorite sports teams, but you have to choose which games to record. Much better on hopper because it just records all future games without ever having to mark that team.
6) Direct tv has a 12 hour skip ahead on menu, so just tapping twice shows you tomorrow night, which is great bumping ahead in the week to see what is upcoming. Dish hopper doesn't have this ability.
7) Deleting shows on dvr is much better on direct tv, stopping an episode gives you an option to also delete, while with dish hopper you have to go back in. Its just not very well thought out.
As far as what I prefer? The top 2 or 3 .... which direct tv is alot better imo.
The remote for both should have a jump button for 30 seconds, 10 seconds, and 20 seconds. Both just have 30 only, but for different sports it will be a big selling point if they had 3 or 4 different ones because football and NHL you often jump 30 seconds ahead, but thats to much for NBA where you often want to jump ahead 10 seconds only.