Dedicated headphone amp vs Headphone socket on amp

I think Synergy here dictate the road to takes... As an exemple i use a old vintage headphone AKG K340, to honor it, i order to replace my Sansui Alpha ( Vintage amp of 100 watts with headphone socket) a very new TOP headphone tube amp from a designer i admire and which is one of the best on the planet ( i will not name it to not disparage even slightly his amazing tube amp ). 

To make a story short, i heard his magnificent tube headphone amp with his dedicated top non linear power supply and in 15 minutes i knew that it will not did any good for my headphone, even with a better clarity because of a way lower noise floor...

I send it back which cost me 200 bucks (insurance+normal fees) I return to the old Sansui Alpha socket which winned even with a bit less clarity but a stunning presence more 3D holographic and no thinness in the mids and bass to shake my body... Conclusion : synergy dictate everything first... 

I never had never thought one second that my "upgrade" could fail with a tube dedicated for headphone TOP in the world... It is the same thing for dac source... Synergy dictated with which one of my 2 dacs i will use with  the Sansui+headphone and for which one i will use the powered speakers... 

This problem of gear synergy exist at all price level...But especially audible with low cost gear piece or past vintage very specifically asking products like my hybrid picky headphone.

Advice: if you are happy with your actual  amp socket for this specific headphone, i advise you to not invest in an upgrade for this headphone... I would buy another headphone instead if you want an upgrade at all cost...

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