Dedicated headphone amp vs Headphone socket on amp

The headphone output of integrated amps and preamps vary a lot. Some very high end brands have terrible output. Your Rega is not one of them. It is known to have pretty good sounding output. 

I have used headphone amps from a $100, and at least a dozen up to $8K. In general, you get what you pay for. $500 is unlikely to get you something better than you have. 

If you want a great headphone system, it is exactly like putting together a great main system. Every component and aspect must be considered in great detail and with appropriate levels of investment. 

I seriously and intently upgraded my headphone system over a ten year period and ended up with the system I have today. You can see it under my user ID in my virtual systems. It is so much better than anything I thought possible until I dropped in the Woo W5LE headphone amp with Takatsuki 300B tubes. I  had six sets of the very best headphones available at the time (Sennheiser 800, Focal Utopia... etc.)  and tried half a dozen outstanding headphone amps... then finally the Woo. It completely changed what I realized was possible. It is very nearly as compelling as my main system. So, there is virtually no limit to how good a headphone system can be. 

@ghdprentice + 1

A really good headphone amp that can drive most any phone is the Rupert Neve RNHP and it's a good value.  I regret selling mine.   Around $500

All really good insights and input provided to the topic at hand. It really does beg the question if the desire is sufficient enough to go down a second rabbit hole with a bespoke headphone system. Just like my reference audio setup, which took the better part of 3 years to complete. The trial and error, the mix and match, the contemplation & temptation of possibly better options and the wheeling and dealing in the audiophile marketplace would begin again. Not sure if the return on investment is worth it given the price cap imposed on such a project. Although I have no doubt the results might be impressive without the restrictions on cost. For now, the Rega Aethos headphone socket will suffice. With an eye on maybe some better headphones down the line.

You can purchase some very nice sounding dedicated headphone amplifiers for very little money, relatively speaking.  You can compare one to your current setup to see if it’s better than the one you’re using now.  Schiit audio offers a 15 day trial period so that you can return the component you purchase and get your money refunded; minus a 15% or 5% restocking fee, depending on the price of the audio component you purchase from them. 

For a little over $100 you can purchase a Schiit Magni headphone amplifier to try in your system for 15 days.  👍