Both have excellent DAC's and offer the option of tailoring the sound by "rolling", one by changing tubes and the other by changing op-amps. I prefer the sound of my Aune, which is smoother and has a larger and more solid sound stage, both of which features work well with my K702's. The Aune Amp is basically a CMOY design, so nothing ground breaking but it does it's job and does it cleanly and efficiently. The Aune's tube buffer stage is the clever bit of the design as it gives you a touch of that "valve sound" by acting as something of a unity gain pre-amp. The STX amp can sound a bit harsh with detailed headphones and is the weakest link of the card but it still manages to sound very impressive in it's price range. The STX II is reported to have a slightly smoother sound so may be closer to the Aune but it does cost a fair bit more.
You make a very sweeping statement there by declaring it to be the best DAC/Amp available under £200. What about the iFi iDSD, or the Epiphany O2D, or the Beresford TC-7533 Bushmaster, or the Schiit Modi / Magni combo? There is great variety out there and some of it is of extremely high quality without breaking the bank. Did I pick the Aune because it's the best? No, I picked it because it suited my AKG K702 - ie. it sounds smooth yet detailed with a large sound stage, a neutral mid range and well controlled bass plus it's a nice looking piece of kit with a large, external power supply. I purposely didn't want a portable setup because few of them are up to driving the AKG's sufficiently well (excluding the iFi). The O2D is an aesthetic design disaster which should be much improved with the O2Di (but that's not available yet). The Beresford doesn't have USB as an input (which I wanted so I could use it off my tablet too). And the Magni isn't a good sound match for the AKG's as while it's very detailed, it's also on the cold side. The Vali would have been a good replacement but that takes the total over £200.