My first impression was that when used with the verb TO LIKE, the adverbs “most” and “best” are synonyms. I received confirmation of this when I checked the definitions in the Oxford English Dictionary and in the Webster Unabridged.
Most…..in the greatest degree
Best……in the best way; to the most eminent degree, the highest degree
Compare the patterns
I like it very much. ….to a great degree; greatly
I like it very well. …..to a high degree (with verbs of pleasing – to like, to love, etc)
I like it more than I like that. …..to a greater or higher degree,
I like it better than I like that. ….to a higher degree, in a more excellent way
I like it most of all.
I like it best of all.
You can see that in each case the meanings are similar.