I've had this experience SO many times. Someone louder has often tried to take over, assuming I was unsure because I wasn't yelling. Or nurses think I don't know what I'm doing because I'm not constantly thinking out loud during a code or trauma. Or people don't even know that the ER doc has arrived at the code in a floor/ICU room because I don't walk in screaming questions and orders.
On the other hand, there was a time when two nearly identically severely injured (but conscious and very aware) patients arrived at the same time, and another attending and I each took one of them in adjoining rooms. The other attending, an excellent EM physician, happened to be the extremely loud and active type. We each did pretty much the same thing with each patient, and afterward, the nurses commented (in my favor) on the drastic difference between the vibes in the two rooms. My patient was calm, had a quiet moment to call a family member before intubation, etc. The other patient received appropriate treatment, but the stress level in the room was palpably higher.
I appreciate the fact that different physicians have different styles, but I would love it if people would not assume that someone who isn't yelling is incompetent. That said, I certainly don't think it's a reason to avoid EM as a career. Just something to be aware of.