I like both of them, but
Mithrandir is definitely my favourite. The fact that he has the Aragorn signet allows you to use him with both
Aragorn, King in Exile, to cancel out his wounding each turn, and
Hard Choice for additional healing. I also find his constant strength more reliable than
The White Wizard's, which depends on an opponent not being able to remove twilight in a skirmish. I usually use
The White Wizard in tank decks, or decks that add a lot of twilight in the maneuver phase, which is made easier in Expanded by followers. Likewise,
Mithrandir is much easier to use in Expanded because of
Shadowfax, Unequaled Steed. In the earlier formats, even cards like
Intimidate will help out
Mithrandir, and in movie you get
Moment of Respite, which helps a lot. You can also increase his vitality with
Narya and
Gandalf's Staff, and then just use Sanctuary healing on him, as he's less likely than most companions to lose skirmishes.
Mithrandir also has built-in Damage + 1, unlike
The White Wizard or
Defender of the West, which helps a lot with finishing off lesser minions early-game.