Why not both? You can easily do both in the same day. Start on Tete Blanche and then run up the Aiguille du Tour.

If I had to choose one, I'd go with Aiguille du Tour. Which route did you have in mind?

And if you do Tete blanche, take the northface, beautifull short climb, i can recommend it.

gr, Peter

If you sleep in Cabane de Triënt and rise early, go to the Teteblanche, (you will pass it anyway on the route to the aiguille du tour) and then there will be plenty of time left to do the Aiguille du tour the same day.

Climb the Tete Blanche and the Petit Fourche together. You can easily head up the Tete blanche then over to the petit Fourche, it doesnt take much time from one to the other and the are usualy climbed together by guides with clients via the normal routes.
It will take longer to reach the foot of the Tete Blanche from either the Albert 1er or the Trient hut thani t will to ascend it.

Allan