The system of mutations does not really vary between the 4-5 main dialects of Welsh. There are some variations in the degree of use of some mutations, but that can vary as much by the age of the speaker as by their usual dialect.
Another factor is the register of language. Sometimes people stick to the the standard mutation rules in more formal writing and speech but drop some of them in informal situations. On the whole, register is probably a more important factor in language variation in Welsh than dialect.