This is a good generalization. In my experience, some solid state amps sound fine pushed into OD and many tube amps don't/can't actually make their claimed power unless they are pushed into OD.
In order for a wattage rating to be meaningful it needs to be accompanied by a distortion figure. For example the power for tube amps is often cited at 5% THD, which is relatively clean, and 10% THD which is perceptibly distorted.
A few examples: Based on various bench tests I have dug up on the internet it appears that Ampeg SVTs commonly make about 270W at 5% THD and Orange AD200B commonly make about 165W at 5% THD. Keep in mind SVTs are are considered 300W amps and AD200Bs are considered 200W amps. Both amps will make more than their rated power but only if pushed into noticeable OD. Generally a good solid state amp rated for 300W will actually make at least 300W, and it will be very clean.
Regarding the usefulness of a tube amp pushed heavily into OD. At some point the amp will continue to make more power, but it won't technically drive the speakers louder. When the amp is making clean power the output will resemble a sine wave. While the output resembles a sine wave, increased power is achieved by increasing the voltage. Increased voltage generates more SPL from the speaker.
When the amp is pushed into clipping, the way it makes more power changes. No more voltage is available so the waveform starts squaring off. The increase in power is partly because the average time the voltage remains at its max value increases, and partly because the density of the harmonics increases.
If the amp is pushed really hard it will cause the power supply to sag, meaning the peak voltage will actually decrease as the power approaches the maximum value. So you can push the amp to the point where an increase in power actually results in a decrease in SPL generated by the speaker.
Also when you push an amp into OD, energy is transferred from the fundamental into harmonics. This is why the low end washes out if you push an amp too hard into distortion. Although it's a bit difficult to comprehend, the squared off wave you see on the output of a tube amp is not actually DC, its a result of the generation of lot's of harmonics.
For the record, I own 28 amps that range in power from 12.5W to 2,500W. 20 are all tube, 4 are hybrids, and 4 are solid state. One of my solid state amps sounds almost identical to one of my tube amps, and many of my tube amps sound drastically different from one another. Rather than worrying about generalizations about tube VS solid state, just try a bunch of amps and buy the one that sounds best to you.
I have a GK 700RB that is rated at 380W at 4 ohms. Below is a bench test video that shows an SVT making 340W at 11% THD (see 10:06 in the video), and 240W at 6%THD (see 10:40 in the video). I own two vintage SVTs and my 700RB is slightly louder clean than the SVTs pushed into distortion, so in my experience watts are watts. Basically my 380W amp is slightly louder than my 300W amps.