Your PQ at the Joey should be just as good or bad as it is at the Hopper, if that helps. If you are seeing a difference between the two, be certain that it is not the settings on the HDTV before calling Dish. Otherwise, do call Dish and report this. It may be a problem with the MOCA or Hopper sending it to the Joey.
In regards to HD PQ, it seems that LIL (Local into Local channels from the Dish Sat) is reported in smaller DMA's as not that good. However, in the Los Angeles DMA with tons of LIL, I am comparing to OTA TiVo and OTA directly into the HDTV, and the LA LIL's are and have always been in excellent HD PQ, none of the compression artifacts reported from smaller cities, and it looks sharp with detail very close direct to HDTV OTA (MPEG is a lossy compression; the lossy MPEG is also used by OTA's.)
Outside of LIL's that can vary in PQ, in general I have found the best HD PQ to be on Pay-per-view channels (the ones that play the movie over and over---NOT referring to the VOD channels because they are not streamed LIVE) and the Premium movie channels (HBO, Starz, etc.). Then not quite as good, but still quite good, are the general interest channels, and in my observation it depends upon WHICH general interest channel it is (meaning a non-premium movie channel). For instance, ESPN is really quite good HD PQ, while ABC Family (mostly watched by teen-age girls) seems to be just a bit inferior. History or H2 seem to stand out compared to the kids channels in HD, for example. When ever I tune to a premium movie channel, I can immediately see the difference. Although, I am still quite satisfied with the general interest channels.
Being aware of Dish dowrezing HD from 1920 X 1080 to 1440 X 1080 (if it is a 1080i source channel as opposed to a 720p source such as ABC and FOX network as only two examples) and of the compression necessary to provide all the HD content efficiently, or, frankly, at all, overall I am satisfied with the Dish HD PQ. 1440 X 1080 is an approved HDTV resolution. In fact, I think there are 9 approved HDTV formats. Don't assume your local broadcasters are sending out full resolution, either, especially if they have matrixed "sub-channels," and they are stuck using MPEG2.
Now, keep in mind that a lower HD resolution does not mean bad PQ nor any of compression artifacts. The bit rate can often play a far more important role in good HD PQ. A local broadcaster sending out full 1080 resolution, but at a greatly reduced bit rate will look far WORSE than a reduced resolution with a greater bit-rate. Resolution is not always the key to great looking PQ.
Also, keep in mind that Dish (and for that matter, one can presume DircTV and Cable) boxes were designed with hardware to take advantage of software that can enhance or allow for Turbo coding or more throughput to allow for more data than your OTA broadcaster could ever do, or, in other words, with the right hardware and chips, a software update can take a down-resolution and low bit rate HD data stream and work its magic in the box and spit out to your HDTV a PQ that looks as if it were SENT with higher resolution and at a higher bit rate. This is NOT the case for your local OTA's because they can't upgrade all the HDTV's out there, like Dish and DirecTV have upgraded their HD boxes at their own expense, to take advantage of the latest MPEG4 codec or its superior successor nor allow for Turbo coding nor any other sort of technology to improve the broadcasters rotten PQ if they have more than a 2 "sub channels" because it would render obsolete (or brick) a number of older HDTV's out in homes. Some of the newer HDTV's can, in fact, decode MPEG4, but the problem is MOST of the HDTV's in homes now can only decode MPEG2,so we're likely to NEVER see MPEG4 or successors widely implemented for OTA, although I can imagine one channel here and there for closed circuit use for a private (possibly consumer) service, but not for what we have today. KTLA main channel was so pristine HD breath-taking until they added This TV, and then it was slight degradation noticed until they also added Antenna TV, and now it looks as soft as all the other local HD's here in LA. That was some years ago.
And don't assume that just because your broadcaster does not indicate any "sub-channels" taking away the limited bandwidth they have to work with. A broadcaster can broadcast sub-channels on it frequency, but it will be down-mapped to ANOTHER broadcasters channel number, hence not so great PQ and no apparent sub-channels.
I would say, really take notice of the HD you are getting, and then compare it to other MVPD sources such as DirecTV and cable companies and see if you notice much of a difference. I would also say that INCREASING the sharpness on your HDTV and otherwise making the proper adjustments (including either turning OFF or ON "Digital Noise" features and other such options) can do a lot to get the HD from a PARTICULAR SOURCE to look really good.
I will say that everyone I've spoken with does say Verizon FiOS PQ is quite impressive, but they have that huge fiber pipe, but they Verizon has pretty much ceased its build-out, so as close as they were to my home, they will NEVER come now.
If you are interested, Google KLCS /KJLH, Los Angeles experiment and subsequent report with OTA shared bandwidth. It has some interesting facts and suprising things learned about the current ATSC (local broadcaster platform) and its possible future. The report was shared with the FCC who sanctioned the experiment in consideration of new rules nationwide for broadcasters that could allow sharing of bandwidth.
Good luck and let us know what happens.