page, there are many different circuit arrangements for condenser microphones, so I can't say how they all behave. Furthermore there is no standard for "9 - 52 Volt phantom powering" so any manufacturer who lists such a specification may seem to be doing the customers a big favor, but in fact any reference to an established powering standard is being evaded in that way.
In general, most microphones that can accept "9 - 52 Volts" are something like a 12-Volt phantom microphone that is designed to physically tolerate 52 Volts. They either are electret ("pre-polarized") microphones, or else they use a DC/DC converter internally so that the capsule is polarized at the intended voltage no matter what you supply them with (within their range, of course). Whether the audio output circuitry benefits from a higher supply voltage than the minimum would vary with the particular circuit design.
Schoeps CMC 6 and CCM microphones have come up in this discussion, and it's worth mentioning that they are something of an exception to the above. They use DC/DC converters, but instead of designing for the lowest allowable voltage and then throwing away what they don't need (i.e. converting it to heat inside the amplifer), they actually sense the incoming voltage and switch the converters to one of two specific modes. As a result they can (and do) conform to both ISO standard 12-Volt and ISO standard 48-Volt phantom powering, with identical audio performance, including maximum SPL.
But when they run at 12 Volts the DC conversion is more efficient, so for battery-powered recording, that would be the preferred mode if you have a choice. (48 V at 5 mA = 240 mW, while 12 V at 10 mA is only 120 mW.)
--best regards
