what's going on with specs?

2 amps that measure the same as long as they are used within their limits will sound the same

Please list the required measurements

Measurements change with temperature, so unless the amp is played at the measurement temperature, they are meaningless.

Measurements are made with static signals, so unless you listen to test tones, they are meaningless.

Signal over noise and distortion. Power v distortion full load at 4 Ohm both channels driven. Frequency response. Get 2 amps that measure about the same driven below clipping will sound the same or at least so close you would have a hard time telling them apart better than guessing. As long as the amp is considered neutral or transparent with a SINAD in the middle 90's up good luck picking which is which in a blind test.

Of the 4 amps the OP mentions maybe and that's a long shot maybe one might pick out the BHK 250 over the other 3 between the other 3 I know I wouldn't be able too.

so close you would have a hard time telling them apart better than guessing

Perhaps some might be guessing, but there are innumerable people who can tell the difference on any program.

In firearms, there a units whose accuracy is so good that they are set aside for competition. These arms may be designated 1:100 or 1:1000 depending on their superiority.

The same is true for many manufactured item: Engines, binoculars, electronics, etc. Manufacturers run Monte Carlo analysis based on component part tolerances. Just as there are 1:100 on the top, there will be the same on the bottom. They meet spec, but will never hold.

I once bought an amp a pal owned based on how it sounded in both our systems. After a couple of weeks, I returned the one I bought as it was sonically inferior. On the bench, both measured the same.

When we shipped systems for recording studios, the final QC was a listening test. Some units were reworked, some binned.

The biggest variable in the determination of how good something sounds when listening to reproduced or actual live music is the human auditory system. Thus, it is not true that 2 amplifiers that measure the same will sound identical, even if they are listened to at different times by the same human. This fallacy is sometimes repeated by engineers but never would never be uttered by a neuroscientist who understands the complexity of the human auditory system.