Life Line

Robert Picardo enjoyed his double role: "I play not only the Doctor, but his programmer, so I achieved a lifelong ambition of working with an actor who I've admired."

When Troi walks in and sees the two doctors, she asks which one is Dr. Zimmerman. She is an empath and would usually sense emotions from the live doctor and nothing from the EMH. She even says this later on when she detects that the doctor's assistant is a hologram. However, since Dr. Zimmerman and The Doctor were in close proximity to each other, Troi may have not been able to detect which one was the human. On the other hand, only the Doctor would be wearing an obsolete Star Fleet uniform, as still worn on Voyager. Zimmerman is a civilian, so it should have obvious which was which.