Less so with the DT990s, and more so with the AKGs.
The headphone output of the CXA60 is rated at 32 Ohms. If we follow the rule of 8 for matching the headphone impedance, then 8x 32 gives us 256 Ohms. What this means is that the headphone output of the CXA60 is good for driving headphones with an impedance of 250 Ohms or more, but low impedance 'phones won't be such a good match.
The DT990 Pros are (I believe) a 250 Ohm headphone. The AKG K712 Pro is 62 Ohms.
When there isn't a big enough impedance difference between the 'phones and the device driving them there can be changes in the tightness of the bass and in the frequency response. In extreme situations where the phones are lower impedance than the driving source then it can look like an electrical short at some frequencies which means almost no sound to the 'phones at all!
Impedance matching is more important than the quality of the components in the headphone amp circuitry. If the headphone isn't being driven properly, then it doesn't matter if the capacitors and other components are higher quality or sprinkled with fairy dust.
The AKGs could really do with being driven from a headphone amp with an 8 Ohm output. The same would work fine with the DT990s since there's a bigger difference than the 8x multiple.