HEGEL H80 DAC upgrade recommendation 2018

I just purchased a Hegel H80 and am new to the "audiophile" world. I am however enjoying my new setup. I’m wondering if anyone with an H80 has upgraded their system to a new DAC where you’ve noticed a significant difference from using the onboard DAC (all things being equal, same speaker, wires, etc.). Please note that I got the amp for $650 so at the time of this post, I want to find a DAC that makes an audible difference but isn’t significantly more in cost than the amp unless the quality is wildly discernable on this amp with the DAC you recommend.. Open to better but older DACs that can be had for less used or any of the Shiit, ifi, SMSL, etc. DACs then please let me know. I really appreciate your first hand experience with the H80 and any recommendation you have to offer. Finally, l’d love to know if you found any difference between using the line or balanced inputs with your DAC. Thanks.

I have owned my Hegel H80 for two plus years, and am investigating a dac upgrade as well.  Currently am using a Bryston BDP-pi digital player into the Hegel internal dac, powering a set of Vandersteen VLR speakers.  Kimber Kabyle interconnect, speaker wire and power cable. Considering Hegel HD 12 and HD25 dacs, although somewhat dated.  Also considering Mytek Liberty, which just received a great review in Stereophile at $995.  Will report back with findings.  
Placed liberty in system tonight.  Beautiful, articulate sound.  Major upgrade to Hegel integrated Dac.  Many thanks to Dave at Audio Emporium for sage advice and wisdom.

Nice to hear about your experience. I have a few questions:
a) prior to getting the Mytek, were you feeding the Hegel onboard DAC with the USB or the SPDIF output of the Bryston BDP-Pi.. and what if any differences did you notice?
b) did you notice a difference when you switched from the stock power cable to the Kimber power cable? Which version of the cable did you get?

b) On the Mytek Liberty, are you using single ended to Hegel or balanced via a converter.?
thanks much and congrats!

A-Both coax digital and optical.  Coax sounded better.
B-yes.  Kimber PK 10.
balanced output.
Did you audition any other DACs before settling on the Liberty?
Mytek was more naturally sounding, with better soundstage.
That’s interesting.  I have an HD25 - very nice DAC.  You’re saying the Liberty was better? Was that with an external power supply? I’ve been thinking about changing the HD25 for a  Liberty or Chord Qutest but can’t decide if the upgrade would be worth the trouble of buying/selling. 
I thought it was better.  The HD25 is somewhat dated and does not support latest streaming, such as MQA.
MQU is not a factor for me and I don't upsample above 24/96.  The HD25 definitely is dated in that respect but I'm only thinking about sound quality.  I'm taking it you use the standard power supply on the Liberty?
I'd go with a Metrum Amethyst, especially if you can find one used.  It's their entry-level R2R NOS DAC, but a good amount of proprietary technology is trickled down from their much pricier models.  I'd think it would be a significant step up from your amp's internal DAC. 

Here's a review FYI...

Best of luck. 

I too have the Hegel HD25. I previously owned the PS Audio Direct Stream and recently tried the Metrum Onyx but found the HD25 more musical. The others may be more detailed but I prefer the warmth of the Hegel.