what muscles does bench press workout?
what muscles does dumbell chest press workout?
is one or the other better?

Both of the them work the same muscle area. The Bench Press is more used then the dumbbell bench press because you can use more weight thus making the exercise better. However, the dumbbell bench press helps more with stabilization, can fix muscle inbalances, and it is used as a replacement when you need to switch things up.

With dumbbells you are using more triceps, more stabilisers and in more significant ways.

There is no significant amount of control required to perform a bench press (unless you are aiming for a 100% perpendicular line), but there always is with dumbbells - every second you are going to be balancing the dumbbells, which are going to want to go in all directions.

It's very good to do both I think.