Measuring Power across a dummy load - use voltage or current?
There are a number of other ways to measure this (eg, dont use any rectification, measure with a ADC that has a samplerate well above your signal speed, and use that waveform to caluclate RMS). 

At the frequencies you are using, with a good resistor, measuring voltage or current should give equal results. There would only be a difference if the current and voltage were out of phase, which requires reactive components (inductors, capacitors or long transmission lines) in your load.  

The problem with your suggestion of measuring voltage is due to the use of the bridge rectifier. This will induce a voltage drop and thus cause an error. In addition, just measuring the peak will only give accurate results if you have a single frequency signal (IE, a sinewave) and a linear amplifier. If either of these conditions are not met, you will not get correct results. 

There are true-RMS power meter chips from various manufacturers (for use in EG multimeters).