It's about the same honestly. Someone says thank you -- you say "It's my pleasure" Someone asks you to do something -- you say "with pleasure" -- not used as often

It's my pleasure->everybody say with pleasure->cowboy say

language just the tool of communication , sometimes we care about it , it's not so easy for non-native English speaker , so if you want to know the different meaning according to different context or environment , you can go abroad to English native country

In my opinion, the different between "It's my pleasure" and "Withe pleasure" is a little bit difficult. your say "we take you Withe pleasure" but "It`s my pleasure to meet you".

what do you want say?