Hello, recently I got my HD800s and upgraded my FiiO E10K to FiiO K5 Pro for that reason. Today I decided to test both Amps side by side, did my best to volume match and was kind of surprised.
With both Amps at the same volume only differences I hear ( on 5k pro) are faster bass (very obvious), less background noise, maybe (big maybe, because it may be just in my head) better instrument separation and super small difference in tonality that can be a volume miss match. I don’t see much difference between E10K and K5 Pro compared to E10K and my phone which is more obvious. All the zings and little details in the music I can spot on both AMPs pretty much about the same.
Am I too noob to hear a proper difference in texture of sound or there isn’t much difference between cheaper dac/amp combos? If I’m wrong I would be happy to hear some tips on how to spot more differences between these 2. Thanks a lot 
Here are a few observations from your anecdote that I hope will help.
First of all, I’d get rid of trying to A/B test anything. It’s not helpful in this scenario, especially with electronics. This is not a concrete problem-answer like 1+1 = 2 where you can make an immediate conclusion. This judgement takes time. Like Steve Guttenburg, I would suggest to take your time. Use one product, I’d say the K5 Pro for a full week. That’s the only thing you’ll listen to, be extremely familiar with it, then revert back. Do you miss the first sound? If so, then you know it was an improvement.
Secondly, you also purchased two very similar products from the same manufacturer. I’m sure they were built and designed with the same goals and design in mind. In addition, they are both still considered a budget product, even though one costs more than the other. I’m sure the design was the same, but with more juice.
Lastly, the fact that you heard immediately differences should tell you something. I am unsure what you were expecting. Did you want something completely colored or magically hear different sounds that you haven’t heard before? If that is the case, you would likely need to get a product that was designed with different priorities.
I hope this helps.
I will go and test Mytek Liberty DAC tomorrow and see how it differs from my K5 Pro. I remember hearing cytek soundkey once that sounded pretty different from e10k at the time bit it was a long time ago. I still expected a bit more difference TBH, E10k is a very old design while K5 Pro came out last year.
Is that Liberty a DAC only or a DAC/amp? Regardless, it should be a pretty good improvement. Do you know if they do a long-term audition where you can borrow it for 7 days with a deposit? That would help tremendously.
Lastly, you should considering improving your amp. You have a nice pair of headphones, one that will scale well and pick up on a lot of detail. I think you will get a lot of improvements with a quality amp.
HD800s already sound amazing but I want to be sure they are playing to their fullest :D. Liberty is a DAC/AMP, reviews are good but not that many.
I haven’t heard an 800s personally, but a lot of people like its synergy with a tube amp. Perhaps the shop has one for you to try?
I cant use tube amps cus of cats 
i have 2 cats and many tube amps
use 2 shelves. 1 for the tube amp to rest on, one to go above it. or, depending on the tube amp, use screws to screw it to the shelf.
I would highly recommend a tube amp for hd800’s.
that being said, there are some good solid state choices these days as well.
schiit asgard plays well with most headphones.
drop just came out with the ifi zen amp not long ago. Specifically designed with senn’s in mind.
If you can not order from drop due to region, I personally own, and like, the ifi zen dac. It has much less power under the hood. But it does have a built in dac that plays well with senn’s imo. And for me, it has more then enough power for senn’s.
You can also try one of the hybrid tube amps off of amazon/ali express. 11/11 is around the corner. No idea what that holiday is, but some Asian companies have massive sales for it. Can get some good hybrid tube amps for cheap.