@flasd Distortion at clipping is why this myth persists. Simply put, tubes can overload quite gracefully while transistors cannot. So you can have the musical waveform briefly overload a tube amp and you may not notice. But you will if that happens with solid state! In addition, 3dB isn't much of a difference to the ear, but to an amp its a doubling of power. For this reason a tube amp that overloads gracefully might appear to keep up with a solid state amp of twice the power.
One exception might be when you try to drive certain ESLs or other speakers that have a high impedance. Tubes quite often do not lose power into higher impedance, but all solid state amps will. For example to make a Sound Lab ESL play at a certain volume, you might need a 600 watt solid state amp to do the job in many rooms. Because the Sound Lab has a 30 Ohm impedance in the bass, that solid state amp might be only able to make about 150 Watts. But a 150 Watt tube amp might make 150 Watts into that same load- and so in that case its not myth; the tube power is more powerful.
One exception might be when you try to drive certain ESLs or other speakers that have a high impedance. Tubes quite often do not lose power into higher impedance, but all solid state amps will. For example to make a Sound Lab ESL play at a certain volume, you might need a 600 watt solid state amp to do the job in many rooms. Because the Sound Lab has a 30 Ohm impedance in the bass, that solid state amp might be only able to make about 150 Watts. But a 150 Watt tube amp might make 150 Watts into that same load- and so in that case its not myth; the tube power is more powerful.