It all depends what you want:
Area of Operation:
Outcasts you have allot bigger Zone of Interest. Operating in more core areas as well as the Border Worlds such as Taus, Liberty and the lot.
Corsairs a bit smaller. Mainly operating in Border Worlds (Sigmas, Omegas, Omicrons) and Bretonia.
Ships:
OC have somewhat faster ships.
Corsairs have more slower ships but they are tanks.
Examples: Sabre vs. Titan and Outcast Gunship vs. Corsair Gunboat.
And a whole lot more. What do you want to RP more and you think will be most enjoyable?