To my ear, "pompous" language frequently correlates with using unnecessary words, or using complicated synonyms of simple words.
Compare: "It is my pleasure to invite you to the party" vs "I am most pleased to extend you an invitation to attend the party".
As other answers have noted, there are appropriate situations for both.
Some further thoughts on this specific example:
"It's my pleasure to..." is a common phrase if you want to be polite.
"I am pleased to..." is also common.
"I am most pleased to..." is NOT commonly used conversationally.
Just some guesses on why this sounds pompous:
Most of the time "being pleased" is binary: either "I am pleased" or "I am displeased".
Comparing different degrees of the adjective
pleased is weird; there are better options. It's not actually incorrect to say "I'm more pleased with the iPhone than I was with the Android" but it's IMO better to say "I prefer the iPhone to the Android."
Because "I am most pleased" is not a common construction, the listener has to do a little bit extra mental work to figure out the meaning (as opposed to using a colloquialism that the listener already knows)
So, IMO, the best phrase for the speaker to A) extend a polite invitation, B) indicate that he is exceptionally happy to invite you, and C) avoid sounding pompous, is:
"It is my great pleasure to invite you..."