They are pretty much the same, you can use them both in formal and informal situations without any difference.
Indeed, "piacere" and "favore" are synonyms (with the meaning of "favour")
Other ways to express it are, as said by JohnnyJo, "per cortesia" and "per gentilezza", which are very much more formal and far less used.
"Cortesia" and "Gentilezza" can be used as abstract nouns, meaning "gentleness" (but this is not this case);
but can also be used as synonyms of "favour", and it happens in the expressions "per cortesia" and "per gentilezza"
Example: il tuo animo é pieno di gentilezza - your spirit is full of gentleness
fammi una gentilezza, portami quel vaso - do me a favour, bring me that vase
I hope that it's clear enough ^^