Dedicated headphone amp vs Headphone socket on amp

As I am fairly new to the whole headphones world. What is the general consensus in regards to superior sq for headphones,  running from an external dac (aavik d-180) to a dedicated headphone amp (no dac) or the headphone socket on a fairly decent int amp (Rega Aethos). I have tried the headphones (sony mdr-f1) from the dac to a small ifi zen can in comparison to directly into the headphone socket of the Aethos and it is a total mismatch. With the latter beating the pulp out of the former. Now, what would happen in a similar matchup with a more expensive headphone amp with a price capped at $400-$500?...In general, is it even worth considering a headphone amp at this price level with the already proficient quality of the headphone socket in the Rega Aethos keenly in mind? .