Is there any study on the relative difficulty of native Chinese speakers with different dialects learning another dialect?
(This may not be a proper answer.)

I don't know if there is any study about that. 

The relative difficulty is based on learners.

For nonnative speakers, they may find learning Cantonese is as difficult as learning Chinese. For Mandarin speakers who were born in the north of China, they may consider Cantonese as difficult as a foreign language. But for people who were born in Fujian Province, they may learn Cantonese easier than others.

There are a wide variety of dialects in China. Usually, people from the same region may understand each other's dialect well. But this is not true in Guangdong Province.

For most Mandarin speakers, they may find Northeast Dialect, Henan Dialect, Tianjin Dialect and Sichuan Dialect most easy to understand.