dream, the amplifier that Schoeps normally recommends nowadays for all phantom-powered operation is the CMC 6--, because it can be used either with standard 48-Volt or standard 12-Volt phantom powering (with twice the power efficiency at 12 Volts--very interesting for people who run their equipment on batteries), and because CMC 6-- amplifiers made in the past several years have better immunity to extreme radio-frequency interference, while the same level of protection wasn't added to the other, older amplifier models.
If I were buying new amplifiers today, there is no question which one I would buy. It's not that the old ones were slouches--I can remember only two RFI problems in 30+ years of using them--but the number of devices that radiate energy at radio frequencies has increased enormously in the past decade, the wavelengths being used are shorter than were commonly in use when the series was designed in the early/mid 1970s, and nowadays your vocalist may very well have a Blackberry in her pocket while she's standing six inches from your microphone.
Apart from that, however, the performance of a CMC 5-- or CMC 6-- with active accessories such as a "Colette" cable is precisely equivalent; neither model is better than, worse than, or different from the other at using them.
--tonedeaf, just to explain some details, since you seem interested in these things (bless your heart): The voltage delivered by any Schoeps CMC amplifier to the microphone capsule (whether or not an active accessory is used, such as a Colette cable), is 60 Volts rather than 48. This gives higher sensitivity and a better signal-to-noise ratio. All amplifiers of the Colette series contain DC converters to derive the polarization voltage from the incoming powering. This includes the CMC 5--, which is designed for 48-Volt phantom powering only. Since its current draw is about 4 mA, the voltage drop across the specified supply resistors is almost 14 Volts, leaving the microphone to receive only about 34 Volts anyway. The same applies to the CMC 6-- when it is powered at 48 Volts rather than 12 Volts.
Prior to 1974 Schoeps made the CMT series of microphones, in which the powering was just as you describe: The 12-Volt models used DC converters to create 60 Volts for capsule polarization, while the 48-Volt models used the input voltage more or less directly to polarize the capsules. But that limited the 48-Volt models to a very low supply current (< 1 mA) so that the voltage drop across the supply resistors wouldn't be excessive. That current limit, in turn, somewhat limited the maximum SPL that the microphone amplifier could keep up with. In addition, the capsules for the 48-Volt versions had to be trimmed a little differently to compensate for the lower polarization voltage, with the result that the capsules weren't fully interchangeable between the 12-Volt and 48-Volt mikes.
The higher-current, transformerless design of the CMC 5-- amplifier allowed the maximum SPL of the microphone to increase to ca. 130 dB, and allowed users to use any Colette capsule and/or accessory on any CMC amplifier regardless of voltage. The CMC 6-- amplifier was introduced many years later, but its 48-Volt mode works the same way as the CMC 5-- in that the incoming voltage is still stepped up to 60 for polarizing the capsule.
--best regards