Question

is there any difference between \mucho gusto\ and \encantado/encantada\?
no, both \mucho gusto\ and \encantado/a\ are formal.
no, both phrases have the same basic meaning can be used interchangeably when meeting someone.
yes, \mucho gusto\ is formal and \encantado/a\ is informal.

Explanation:

Both "mucho gusto" and "encantado/encantada" mean "nice to meet you" in Spanish and are interchangeable in meeting - someone contexts.

Answer:

No, both phrases have the same basic meaning can be used interchangeably when meeting someone.