Well, I am all for reduction in snobiness.
There are some instances where the 600 ohm DT880 might sound better- and that is when used with some OTL tube amps with rather high-ish source impedance. YMMV!!!
- The 600 ohm 'phones won't load the amp down a whole lot- these amps want to deliver voltage, not current so much. So the amp should maybe sound a little better- MAYBE. (I am thinking Bottlehead Crack here- they like higher impedance 'phones.)
- The 600 ohm 'phones will damped more on these amps than the 250 ohm ones. Now, this is an electronics 101 type Ohm's law kind of thing, the math shows more damping, not sure you can hear this.
So, maybe the 600 ohm 'phones could sound a little better in these instances. The operative word here is MAYBE.
I had the 250 ohm DT880's, I sold them and got the 600 ohm. But I did not sell them because of impedance- I sold them 'cause my old 250 ohm ones had a very fancy rather costly and REALLY REALLY STIFF cable on them. I COULD NOT STAND THAT CABLE, IT HAD A MIND OF IT'S OWN LIKE A SNAKE. The cable was fancy and $$$, like I said, so I sold those phones and bought a new pair of DT880's with the stock flexible cable. As long as I was getting a new set, I opted for 600 ohms- because MAYBE they will get along just a smidge better with my Bottlehead Crack/Speedball amp. Maybe. In theory.
Maybe they do. Without the old 250 ohm headphones for A/B, I dunno. The new 600 ohm jobs sound good on the Crack. So did the old 250 ohm ones. The DT880 is my favorite "premium-but-not-top-of-the-line" headphone. And they are just about THE most comfortable headphones I have.
So the sound is maybe improved. Or maybe it isn't. But WOW do I like the "regular" cable, it hasn't tried to strangle me once, nor has it tried to flip my amp off the desk. Which the old cable routinely tried to do.
Or maybe not!