Alanya is defined by its castle, which sits on a rocky peninsula jutting into the sea, with the town spreading out on either side. Down by the harbour stands the Red Tower (Kızıl Kule), and at the foot of the peninsula is Damlataş cave. Long sandy beaches run away from the centre in both directions, including Cleopatra Beach on the west side of the castle.
Marmaris is defined by water of a different kind: a large natural bay with a marina at its heart. The town wraps around the bay, and its neighbours İçmeler and Turunç sit further along the shore.
In short, Alanya is a castle-and-beach town; Marmaris is a bay-and-marina town. Which picture appeals to you is a useful first filter.