Hi. I posted in this thread during a time when my day job had me in a state of great anxiety, and my focus here was lousy. Begging the forum's pardon, I'm rewriting some of my old messages.
Every condenser microphone has an amplifier circuit, and every amplifier circuit has some inherent noise. The one and only possible technical advantage of a larger diaphragm is--all other things being equal--greater capacitance, which means a greater ability to shunt (i.e. reduce) the input noise of whatever active device (tube, FET) comes first in the circuit. This is why the first commercially available condenser microphones for studios back in the late 1920s were large-diaphragm: All active circuitry was tube back then, and low-noise tubes hadn't been invented yet.
Now, in reality that all-important "all other things being equal" proviso can't be relied upon at all. A microphone with a large-diaphragm capsule may be no quieter than any given small-diaphragm microphone that you might be considering; it may even be noisier. For a number of reasons (cost being a big one) most microphones aren't as quiet as they could be, and the amount of extra noise they each have is a real variable. The world's quietest microphones are large-diaphragm, but the quietest small-diaphragm microphones are quieter than many large-diaphragm microphones.
The thing is, for most people who do live recording, the noise levels of the venues where we record exceed the inherent noise levels of our microphones significantly, so we never hear the noise of the microphones. Thus the one technical advantage that a large-diaphragm microphone could have doesn't matter audibly to us, even if that potential is fully realized.
Before I leave the topic of noise, I have to say that the spec-sheet comparisons that we can make as consumers are fundamentally unreliable. This is a widely recognized problem within the industry. A-weighted rms figures are worse than useless; don't even bother looking at them.
But even the best manufacturers don't measure microphone noise the same way. A few years ago, a working group of the AES sent a set of a dozen microphones around to various manufacturers (including Neumann, Schoeps, AKG, DPA, AudioTechnica and others), and asked them each to measure them and report on what they found. The noise measurements varied by up to 6 dB for the same individual microphones. Those were the results that the most honest, serious manufacturers got with the best equipment and procedures, while all the other manufacturers on the committee were watching and comparing the outcomes. And there certainly are manufacturers whose marketing departments aren't as scrupulous as these engineers were.
--best regards
P.S.: I also have to say that all other supposed advantages that are claimed for large-diaphragm microphones, in this thread or elsewhere, are either illusory or just plain wrong. The prime example of that is their (supposedly) better bass response. I'll get to that in another message, though.