They claim an amp with higher power would produce more bass/a warmer sound at the same listening volume, if I've understood things right.
I am certainly not an expert either but have learned a few things at ASR and can comment on this point... A higher power amp does
not "produce" more bass at a given listening volume. What happens is the bass are at higher levels than the rest of the frequency range on almost all the music tracks produced by humans. So, if an amp is limited in power, the bass tend to suffer first (audible distortion, or lacking altogether).
The HD650 is a high-impedance HP, but in addition, it's impedance is variable: around 320 Ohm from 1kHz to 5kHz, and as high as 480 Ohm at 100Hz. This can exacerbate the issue of an amp that is voltage-limited (and other things if the amp has a high output impedance). That being said, the HD650 is not particularly "ineficient" and it does not need very high voltage & power to produce loud levels--hence
@staticV3 and
@Elitzur–Vaidman comments that an Apple dongle can drive the HD650 adequately.
Going back to the DX1 question and the DX3 Pro+ recommended by
@Matias:
- The DX1 can produce 11Vpp (high Gain), which is more than enough to drive the HD650... very loud!
- The DX3 Pro+ can produce 21.5Vpp (high Gain), which is enough to drive the HD650 to... insane levels... blow your tympans... blow the headphone... or all of these !!!
If you prefer the DX1, because it's cheaper and more compact, go for it! If you can afford the DX3 Pro+, go for it! I am sure they are both fine, but I am also confident you will hear "differences": the DX1 will sound "warmer and more rounded" because... it is compact, cute, and has an AKM chip !!!
The DX3 Pro+ will sound "cleaner, more technical"... because it is more expensive, it has an ESS chip, and it's technically better !!!
I am sure that there won't be any difference and both are going to be "transparent"... so, go for the one that put the biggest smile on your face!