Both.
Not only do both approaches have their merits and advantages, but there are also gray areas (real time games that proceed so slowly they might as well be turn based), but also games that utilize both to great effect. Usually, this means that a broader Strategic view is in one of the two forms, while the narrower Tactical situations are in the other.
For instance, Total War series uses Turn based for its Strategic map, while the individual battles are played out in Real time. On the other hand, the old XCOM games (the REAL XCOM games) used a Real time Strategic map and Turn based tactical missions.