Here are the differences I found:

19 Red - The new H3 remote does not have colored buttons. It has an OPTIONS button instead and this is the code for that. The 4 color buttons continue to work on H3 however. It's just that Red is always the first selection.

23 Swap is no op on H3 (61 but PIP Swap does work)
38 # (Search) -- # is 3 (Help) on H3
39 Discrete Off behaves as Power ON on H3
41 SAT -- on H3 turns off the "remote mode reminder" message
42 on H3, turns on the "remote mode reminder" message
47 Recover is no op on H3
52 Dish (VOD on H3)
56 System Wizard is no op on H3
58 is PIP menu on H3
60 PIP Side by Side is no op on H3