Much more is okay, but using it with much more difficulties is not. (Even much more difficulty is a bit odd.)
There are many word choices here, all depending on your intent. I will try to provide a few examples.
The second experiment involved extra computation, resulting in a much more difficult process than the first.
The second group of experiments requires additional computations; in comparison with the first group of experiments, these computations are much more difficult.
The experiments in the second group, because of extra computations, are much more difficult.
The second experiment added a complicated computation that presented a much greater degree of difficulty.
Note: You can add extra cheese to pizza, and you can add extra data to a mobile phone plan, but I believe that to add extra computation[s] in this context sounds a bit redundant. (I would say there are extra computations, there are added computations, or I will add another computation.) However, that may just be my personal style.
I didn't understand what you meant by with one of the first one as it related to the overall sentence, so I didn't try to interpret it.