You'll never get consensus. It's all just parroting and confirmation bias.
From a purely technical standpoint assuming "perfect" amp behaviour and no other variances, the higher impedance model "performs" better.
Subjective impressions is pretty much a crapshoot, though you can draw general trends from the technical data
- If an amp can't provide sufficient power (hard limit either through current or voltage), the sound will be jagged and harsh due to higher order harmonic distortion generated as a result of a chopped waveform (I won't bore you with the math behind that)
- If an amp can't provide sufficient power (soft limit, generally current or built in compression), the sound will be mushy and weak, transients and impacts will be soft
- Headphone impedance varies quite a lot in the Beyerdynamics; if memory serves it peaks around 100Hz. If you have an amp with high output impedance, this plays a little bit with the frequency response due to how the voltage division works. Sometimes people like this, sometimes people don't.
- Headphone impedance also affects damping factor, but whether that is actually relevant for headphones and whether people like that is up for debate.
- Headphone impedance varying also results in varying damping factor for complex fun and games. Meh. Some would also call this a red herring because typically damping factors are so high in headphones anyways that it hardly matters, vs the speaker world where impedances are lower. The issue crops up more when you're running tube amps with high output impedance, but then you're into wildly different amping philosophies and intended sound, so again... Meh.
- Sometimes the higher impedance models cost more. That often leads to confirmation bias.
- Higher impedance, higher numbers, rarity, gives people the humblebrag and more confirmation bias.
Me personally, I've owned or heard almost every single variant of the DT770/880/990, as well as the Sennheiser HD25-1/13. Provided sufficient amplification, I have universally preferred the higher impedance models. I'm an educated and experience data point, but only a singular one. Double Meh.