The empty struct and empty interface, though syntactically similar, are actually opposites. An empty struct holds no data; an empty interface can hold any type of value. If I see a map[MyType]struct{}, I know immediately that no values will be stored, only keys. If I see a map[MyType]interface{}, my first impression will be that it is a heterogenous collection of values. Even if I see code storing nil in it, I won't know for sure that some other piece of code doesn't store something else in it.
In other words, using struct{} makes your code much more readable. It also saves a little memory, as described in the other answer, but that is just a fringe benefit of using the right tool for the job.