Maybe I can add my 2 cents here
I have 3 little-dot Amps. A Little-Dot II+, A Little-Dot II++ (Immediate predecessor to the MKII), and a Little-Dot I+.
The II+ and II++ are both full tube units and deliver more power into high impedance headphones. The I+ using transistor output, delivers much more power into low impedance headphones.
I have a number of different headphones. My lowest-impedance headphones are my Sony-XB700s at 24ohms, and my highest-impedance headphones are my Beyerdynamic DT990-Pros at 250ohms.
Using the 250ohm DT990-Pros on the Little-Dot I+ works fine. The difference is that I have to turn it way up, past noon on the dial for it to really get loud and even then, heavy bass ultimately just lacks punch and impact. The amp is really running out of gas at that point, and you can tell. It doesn't sound bad, but it doesn't really sound great either.
The Sony XB700's however, at 24ohms, the I+ is delivering almost an entire watt into these suckers. The amount of power it is able to pump into these headphones is truly breathtaking, because they are very well matched.
Just the same, my preferred amp for my 250ohm DT990-Pros is my older Little-Dot II+, a DHT tube design that is good for about 600mw at 250ohms and these DT990's really come alive. They absolutely can handle more power than the specs say and I pump that into them hours on end every single day. The bass is clearly more defined, with impact and punch that the I+ lacks (when matched with the 250ohm cans).