I wouldn't expect miracles from 4K upconversion, but its not bad. The size of the TV will make a difference, especially if you are moving to a TV considerably larger than what you are used to. The larger the TV, the more imperfections you will notice from the Dish compression at the same viewing distance.
As for the Hopper 2000 vs Hopper 3. The picture on regular HD channels will be very similar on the new TV, as both are going to output up to 1080i and your TV's scaler will handle the upconversion to 4K. While the H3 does display 4K content, it only outputs a 4K signal when viewing 4K content. The rest of the time it only outputs 1080i signal just like the original Hopper. That said, the H3 is light years faster in operation from the original Hopper. Its a worthy upgrade on that alone, IMO.