One doesn't exclude the other. A better DAC will be a better DAC, a better or just more adequate amp pairing can have various consequences, and affect some variables positively(objective for sure, subjective usually, subjective strictly because of sound, sometimes^_^).
But we get much bigger impact and potentially much bigger improvement when we care for the element with the least fidelity and consistency. That weak link, as we both said because it's an easily tested and testable fact, is the headphone.
@TurboDorkDon sorry about the useless scene(2 people talking past each other don't make a conversation). IMO the best advice given so far has been to get lots of music.
Second-best advice, IMO, was telling you to go try many rigs, anyway you can(meets are probably the best way to listen to all the new expensive FOTM audiophile devices from whatever country).
Because no matter how perfect and all knowing an audiophile want to imagine himself, we usually take a long time figuring out what we are really looking for. And we also inevitably end up with extra non audio priorities. If I can't make my mind between gears, the final choice will probably be about plugs, the volume knob, or if a LCD screen has a blue-ish backlight(I not a fan of green, and I very much dislike yellowish ones). I bought a camera that can turn on the LCD backlight at the top at night, and it breaks my heart anytime I use that yellow monster. It's trivial, but also not.
Related, but that's an even more personal opinion; if I was starting from scratch with money burning my pockets, I wouldn't get a rig listed by audiophiles. Not that Headfiers lack important insight and experience, or that the suggested rigs are crap, but simply because it's exactly what I did when I first got into the hobby, and I've regretted nearly all my initial purchases done that way(for audio but also non audio reasons). It's one anecdote, and maybe just bad luck, but I at least would not do that again. And that is why I find so important to go try a bunch of gear yourself.