One quick point difference I have noticed with my current setup about Logmein and RemoteDeskTop, is that with LMI I don't have to sign on/off when I go from laptop to my office computer (main computer) and with RDT I do, which is a bit inefficient.
This is actually a security feature. So no one can see what you're doing with your computer. It just locks the computer when you login. Technically, that's how it should be done. With an SSD, I can lock and resume in less than a second.
If you don't like typing in the password, you can get a fingerprint reader or something or remove the password. (The patch has an option for that, but it would be dangerous to use.) The multiple sessions will let you run two concurrent sessions. Two separate instances of AC, so you would have to look up the patient when you got back to the room. You could use something like UltraVNC over the LAN too if you just want to see your screen.
So lots of choices. You can decide what you think is best.