In my opinion, it`s particularly the same. If you miss out on something you don`t take part in a good opportunity to enjoy or get something useful. (I missed out on the party= I wish I had gone to the party to have a ball)
To my mind, "miss the party" and "miss out on the party" is particularly the same. The only difference can be that in one you are emphasising the fact that it was a fun party, while in the other you are just saying you didn`t go to the party.
Interested in Language