Over the decades, the best performances I've heard of this sonata have come from the following 4 pianists: Rudolf Serkin, Sviatoslav Richter, Emil Gilels, & Youra Guller. (I've not heard Myra Hess, but her Op. 110 has a strong reputation.) However, in the case of Richter & Serkin, it's difficult to pick a best performance, as there are numerous recordings, in varying degrees of sound quality, & I've not heard them all.
1. For Serkin, I've particularly liked his "unreleased" recordings, which his son, Peter, permitted to be issued after his father's death. Serkin's 'unreleased' performances of Nos. 30 & 31 are exceptional--desert island discs (for me)--whatever their minor flaws may be otherwise (which I gather are what prevented Serkin from releasing these recordings during his lifetime).
https://www.amazon.com/Serkin-Unrel..._1_1?s=music&ie=UTF8&qid=1524346356&sr=1-1&keywords=Serkin+beethoven+unreleased
Serkin's later recording for DG was made towards the end of his life at a Carnegie Hall concert in the 1980s. Again, whatever the flaws, and I've heard people complain that Serkin was technically past his prime by this time, his Op. 110 is nevertheless a deeply insightful and beautiful performance, IMO. If interested, you can hear it on You Tube:
In addition, there is an earlier CBS/Sony Serkin recording, which I've not heard, and the 1960 BBC recording that Mandryka mentions, which I've also not heard:
https://www.amazon.com/Beethoven-So...1?s=aps&ie=UTF8&qid=1524351003&sr=1-1-catcorr&keywords=Beethoven+serkin+op.+110
https://www.amazon.com/Beethoven-So...=sr_1_1?s=music&ie=UTF8&qid=1524351003&sr=1-1&keywords=Beethoven+serkin+op.+110
2. With Richter, there's a late Op. 110 performance on the Russian Revelation label that is excellent, and a live performance from Prague that is remarkable. But perhaps my favorite Richter Op. 110 comes from a 1963 concert in Leipzig, as I tend to find Richter's best period to be the 1960s:
https://www.amazon.com/Richter-Leip...A85TCE3X20KG8910&pd_rd_w=lZdDu&pd_rd_wg=BLII9&psc=1&refRID=WFJNA85TCE3X20KG8910
https://www.amazon.com/Richter-Leip...sr_1_2?s=music&ie=UTF8&qid=1524346761&sr=1-2&keywords=Richter+beethoven+leipzig
https://www.amazon.com/Beethoven-La...=UTF8&qid=1524346859&sr=1-3-fkmr0&keywords=richter+beethoven+russian+revolution
https://www.amazon.com/Beethoven-Pi...usic&ie=UTF8&qid=1524346886&sr=8-2-fkmr2&keywords=richter+beethoven+prague+sacd
https://www.amazon.com/Sviatoslav-R...0_1?s=music&ie=UTF8&qid=1524347234&sr=1-1-fkmr0&keywords=richter+prague+0p.+110
3. As for Gilels, I've found his Beethoven was often better live in concert, though I don't know if there are any live Op. 110 recordings from him?--perhaps from the Russian archives box set, or from Meloydia or Doremi? However, if so, you're probably dealing with a lesser sound quality. Fortunately, I think very highly of Gilels DG studio recording of Beethoven's Piano Sonatas Nos. 30 & 31, which was the last recording he made before his untimely death in the mid-1980s:
4. Youra Guller's recording of Beethoven's Nos. 31 & 32 for Nimbus is another desert island disc in my collection, and no matter how many versions of the Op. 110 sonata you may have, Guller's is essential, IMO.
https://www.amazon.com/Piano-Sonata...ef=sr_1_2?s=music&ie=UTF8&qid=1524347649&sr=1-2&keywords=Youra+guller+beethoven
https://www.amazon.com/Beethoven-La...ef=sr_1_3?s=music&ie=UTF8&qid=1524347649&sr=1-3&keywords=Youra+guller+beethoven
https://www.amazon.com/Beethoven-Pi...ef=sr_1_1?s=music&ie=UTF8&qid=1524347649&sr=1-1&keywords=Youra+guller+beethoven
5. I've also liked Annie Fischer's late Beethoven too, but she only recorded Nos. 30 & 32 early in her career (for EMI), & Fischer couldn't consistently play through difficult pieces late in her career without making lots of noticeable mistakes. So she ended up painstakingly recording her Beethoven cycle for Hungaroton piecemeal, that is, one small section at a time. In other words, they are heavily edited performances, unusually so, even if Fischer does have a very deep understanding of the music:
https://www.amazon.com/gp/product/B00LO6A51S/ref=dm_ws_sp_ps_dp
6. On period pianos, I've liked both Ronald Brautigam and Penelope Crawford in Op. 110, but haven't explored any others:
https://www.amazon.com/Beethovens-P..._1_3?s=music&ie=UTF8&qid=1524347796&sr=1-3&keywords=penelope+crawford+beethoven
7. Finally, most recently, I liked Igor Levit's Op. 110 recording for Sony. Levit brings a more Baroque-like feel & touch to Beethoven, which I can find interesting, particularly in the more fugue-like movements, such as in the Hammerklavier, where clarity is so important:
https://www.amazon.com/Beethoven-La...8687C/ref=sr_1_1?s=music&ie=UTF8&qid=1524347820&sr=1-1&keywords=Levit+beethoven
So, there's a lot to choose from. Even though it's a pity that neither Bruno-Leonardo Gelber or Arturo Benedetti Michelangeli ever recorded this sonata, as they're two of my favorite Beethoven pianists.
P.S. Historically speaking, I've not heard Edwin Fischer's Op. 110, or Wilhelm Kempff's pre-war APR recordings either, but would imagine they're very fine. And, of course, there's also two recordings of Op. 110 from Artur Schnabel, who tends to struggle in the more difficult passages, but plays the slow movement with incredible beauty.
https://www.amazon.com/gp/product/B071LK4QK2/ref=dm_ws_sp_ps_dp
https://www.amazon.com/Beethoven-La...1_1?s=music&ie=UTF8&qid=1524350475&sr=1-1&keywords=wilhelm+kempff+beethoven+apr
https://www.amazon.com/gp/product/B007FST7GS/ref=dm_ws_sp_ps_dp
Hope that helps.