Pandas MultiIndex versus Panel
In my practice, the strongest, easiest-to-see difference is that a Panel needs to be homogeneous in every dimension. If you look at a Panel as a stack of Dataframes, you cannot create it by stacking Dataframes of different sizes or with different indexes/columns. You can  indeed handle more non-homogeneous type of data with multiindex.
So the first choice has to be made based on how your data is to be organized.
Using Pandas, what are the reasons to use a Panel versus a MultiIndex DataFrame?
I have personally found significant difference between the two in the ease of accessing different dimensions/levels, but that may just be my being more familiar with the interface for one versus the other. I assume there are more substantive differences, however.