The SinglePower amps can drive all impedances without a transformer. The RKV can be noisy with low impedance cans, unless you use the Impedanzer, and outboard transformer. The RKV will change slightly with different tube brands, while the SinglePower amps can change dramatically. This is due to the DC Servo control in the RKV. This linearizes the output of the tubes, at the cost of some of the high-end "air". The SinglePower amps are simply better in the midrange and highs, at least with decent tubes. The RKV has a much higher power output, however, and can drive a K-1000, which the SinglePower amps cannot do. If that's your headphone, the choice is easy.
IMO you get almost everything the RKV offers, plus a degree of transparency the RKV cannot do, even with the stock PPX-3. As you move up the SinglePower line, some of the tube euphony is traded off for increased detail. These amps are capable of retrieving information that the RKV just doesn't reproduce.