Well, when you’re listening to content that’s coming out of the headphones in the Tcoil only mode, there’s really no noise per se to worry about something such as the signal to noise ratio in the first place, unless you’re talking about the floor noise when there’s no sound from the content. But in this case, during moments when there’s no sound from the content and you don’t or can only barely notice the floor noise, then the floor noise is really not any issue to be concerned with.
The only reason that you want the Tcoil and Mic option when listening only to content from the headphones is only if you want to be aware of your surrounding sounds and don’t want to be isolated 100%. For example, you want to hear the phone ring, the door bell chime, a clock alarm, somebody calling your name, etc. Technically, those sounds would be the “noise” that you want to tune out if you want the best signal to noise ratio, no? So why turn on the mics to let those sounds in?
I would surmise that music sounds better on your over the ear headphones with both the Tcoil and mic turned on is because it would give you a volume boost from both the sound that the mics pick up, and on top of that, the sound that the Tcoils pick up, albeit they’re really the same sound from the same content. I’m just guessing that maybe if you use Tcoil only with no mic, then turn up the volume so that it’s as loud as with the Tcoil + Mic option, then perhaps it’ll start to sound just as good. But that’s just a guess, of course. There might be other factors at play as well, although I can’t really think of any right now.