A Watt is a unit of power or 'work', just like Horsepower, torque, Btu, etc and each is calculated using existing factors. In the case of Watts used as a measure of amplifier power, it's found using voltage, current and resistance so for a given resistance, the voltage from each amplifier would need to be equal for them to be considered 'the same'. The amplifiers would require different input sensitivity in order to produce one Watt with the same input voltage and the amplifier's gain is usually shown in the specs (if the manufacturer chooses to show it).
Generally, a Watt is a Watt, unless the amplifier's design makes its performance dependent on the speaker load and that's really not a great thing- if the speakers cause the amplifier to change its output signal, it's not a good candidate when speakers are changed frequently, it makes finding the 'right' speakers much more difficult and it may not be reliable.