We don't currently know what all the mission pass is used for, but assuming premium is the same as it is with the Japanese release, it entitles you to (shamefully paraphrased from Bumped):
Two different "my room" layouts. You have a mini room by default, but can expand it and have two different layouts.
It enables item trading between characters. You can privately trade items with other premium players.
You earn twice as many FUN points and login stamps.
Access to both premium and team storage. If you have items in premium storage and your subscription runs out, your items will remain in storage until removed. You cannot, however, add any more items to premium storage without having an active subscription.
Gives you access to player shops, allowing you to sell items you don't want or need to other players. You do not need premium to purchase items off of the player shop. It is only required for selling.
Access to premium-only blocks. This means even if your ship is congested, you should be able to access blocks reserved for premium players at peak times.
You can have up to 40 active missions (client orders) instead of 20.
You have access to premium-only drinks from the drink vendor. Drinks give you mission-long buff(s).
You can save up to 40 symbol arts instead of the max default of 10.
You get three more crafting lines for a total of six instead of three. I am not familiar enough with crafting to be able to give you more specifics.
You can accept two more collection files. Collection files are used to work towards powerful gear drops over time.