I know, if you join the Stormcloaks, you get a Stormcloak Officer Outfit near the end. However, is there any special Legion outfit and does it depend which type you picked?

You get to choose what armor the smith makes for you after you join.

I know that, but I'm asking if there is a special armor for them like Legate armour or etc.

Sorry, I got attracted here by your D.P.

As for the legate armour, not sure, but I looted my own stormcloak commander set from Ulfrics right-hand man.

You get exactly what I told you. Thats it.

If you walk in to the Commander's Office of any the Fort you captured, you get to pick up an Imperial Officer's Helm on the table with the map. That is the only difference between the costume of a Legate & a Legionnaire, if you go down the heavy armour part.

I r dissapoint

In saying that, at high level, the general was rewarding my character with Enchanted Daedric Longswords, so it is pretty rewarding.