A little more specific answer to your question: In the case where 150 W + 150 W = 250 W. The full bridge connection will naturally double the voltage. If the load resistance also doubles to 16 Ohms, then there is no more stress on the output transistors than the half bridge connection at 8 Ohms, and the full bridge connection produces twice the power into 16 Ohms as a half bridge amplifier produces into 8 Ohms. When the full bridge is connected to the 8 Ohm load, the stress on the output transistors is higher, at any power level, than it is for the half bridge case.
Here are the numbers for the 150 W + 150 W = 250 W case: One amplifier requires 49 volts, peak, to produce 150 W, sine wave power, into an 8 Ohm load. Therefore, the 150 W amplifier must have a power supply bus of +/-51 VDC or greater. Into a resistive load, the current peaks at the peak voltage. The peak current into the 8 Ohm load is 6.1 A peak at 49 V peak. At the peak output voltage, with 49 V across the load, the transistor has only 1 V across it. 6.1 A * 1 V = 6.1 W of instantaneous dissipation in the output transistor. Now this is not the power dissipation of the output transistor for the whole cycle, just what occurs at the peak output voltage. With the full bridge connection, at 250 W output, 63.3 V peak, and 7.91 A peak are required. Now since each amplifier in the full bridge is producing only half the output voltage, the voltage drop across each power transistor is 51 VDC - (63.3/2) = 19.4 V, at the peak of the output, sinewave, waveform. The output current is 7.91 A, so the power dissipation in the output transistor at this point on its load line is 19.4 V * 7.91 A = 153 W. It is worth noting at this point that the popular misconception that a more powerful amplifier works less than a less powerful amplifier is actually the opposite.
With a limited FBSOA in the power transistors, the manufacturer using a regulated or tapped power supply may reduce the power supply voltage for full bridge operation, to reduce FBSOA stress in the outputs. The 250 W full bridge amplifier would require a power supply voltage of +/- 33 VDC.