It's the freaking ED, all kinds of attendings and residents and medical students will be running in and out of rooms all night.
I've been shadowing in our Peds-ED for almost 4 months now, and I've probably followed 8 different attendings and 18 of the 22 pediatric PGY-1s and PGY-2s into patient's rooms. Of course, I tend to gravitate toward specific ones, and they are probably the ones I will ask for recs, but it is great to see each one handle the same situation in different ways.
To give a more sober answer, I'd highly recommend working with both attendings and residents. Obviously, if you go into emergency medicine, you will spend most of your life as an attending, so it is best to see what it is like to be an attending, but you will also spend 3-6+ years as a resident/fellow, so it is a good idea to spend some time with them too. They will most likely be the ones doing most of the history gathering, which is a crucial skill to learn, and any experience you gain in that is wonderful. But honestly, if you are officially shadowing an attending and he is typing up a chart and a resident gets up to see a new patient, I highly doubt anyone will give it a second thought if you get up and follow the resident into the room, or the nurse taking a fetal heart rate, or the neurosurgeon giving a consult, or the urgent care physician suturing a split lip, or the medical student going to the Rads resident's room to get a read on a CT, or anyone else who happens to find their way into the ED. I specifically e-mailed the Peds EM chief, so he was able to officially give me the freedom to do whatever I wanted (legally), but even if you don't have that direct permission, I'm sure you will do fine. I'd recommend going to the top, and then schedule yourself around a specific attending/resident if you want, but I doubt it is necessary; most physicians are actually pretty nice about sharing you 😉. And if you click with one of the residents and think he can give a wonderful letter, great. If you can get a rec from both an attending and a resident explaining things from their particular view point, even better.