There are essentially two types of amplification used in most headphone amplifiers on the market, voltage mode and current mode, with the vast majority using voltage mode. Generally speaking, if you look at most of the difficult to drive headphones on the market, you will encounter low sensitivity, low impedance Planar drivers, or high impedance dynamic drivers.
Without going into too much detail regarding all of this, the high impedance dynamic drivers (Like the DT880 600ohm) need current more than absolute voltage to perform. So you can have an amplifier which provides less absolute wattage, but at a higher current power such headphones.
Most of the high power amplifiers on the market now feed the power through either XLR, or 4.4 mm balanced connectors, with the ¼ inch jack only able to produce a small portion of the total power of the unit. The issue facing me was that, of the several headphones I own, the two previously mentioned Beyerdynamic models are far and away my favorites.
The 600 Ohm dynamic drivers in the DT880 require a lot of power, and that headphone used only a single ended, ¼ inch connector. This is also a problem as most single ended amplifiers can only accept RCA input, which is generally 2 volts, whereas XLR inputs are 4 volts.