Lee: Flairs the mouth of the case. Length of the case is critical for uniform results.
Lyman 'M': Flairs the mouth of the case and expands the entire neck of the case. It is less critical of case length variations.
For thin walled, long neck, black powder era cases like .32-20, the 'M' die would work best. Die sets that use the 'M' do not have an expander ball in the sizing die. The expander ball tends to stretch the cases.
For modern cartridges with thicker brass and short necks, either would work.