A1 is just an amp. You can always use an external amp with a sound card as the DAC. ST/STX's D/A is pretty good.
Some people say Beyerdynamic designed the older gen of large cans around the ~120 ohms output impedance "standard" and sure enough, A1 has 100 ohms output impedance (most devices are lower like sub 1 ohm, where with some headphones and especially IEMs, it makes a difference; STX is around 10 ohms). The output impedance will color the sound slightly on those headphones, very minimally because the headphone impedance is very high—we're talking something like 0.25 dB effective bass boost in midbass.
Anyway, A1 is a dedicated headphone amplifier that cost quite a bit more. It must sound better, right?
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Nah, it's cans that make almost all the difference in sound, especially once you're past the incompetent range** of amps and DACs (or there's some big issue with output impedance for a certain set, which isn't happening here), and something like STX is definitely past that range. Okay, maybe incompetent not the right word. Lots of expensive audio gear intentionally colors the sound to make it different. That's lower fidelity but whether you like that is up to you.
However, without an external device, you won't get any audiophile street cred from many users in this subforum and elsewhere. Also, external amps can look pretty.
Also, having a nice volume knob and thing to interface with isn't bad.
Here I'm talking about sound quality and not perceived sound quality. Getting the right perspective and frame of mind helps perceived sound quality more so than the usually minute differences in sound waves produced, so if the gear is helping you psychologically, go for it.
Any particular reason you're looking at this one as opposed to something else? Beyerdynamic name? Even talking relative to other products and not headphone or say ear / aural system performance (headphones are usually an order of magnitude or more worse at certain key things), the amps and DACs from the big headphone companies don't seem to be that popular for whatever reason.