5AS4A vs. 5U4

I have a Cary SLI-80 that uses Sovtek 5U4 rectifiers. I am wondering if anyone has had any experience replacing this tube with 5AS4A rectifiers, which I believe is an older iteration of the 5U4?
I have Mullard 5AS4s in my SLI-80 and they sound wonderful; much better than the RCA 5U4GBs that I had been using. At first the RCAs impressed me with their dymanics. A much "juicier" sound. However, the highs were somewhat harsh and hurt my ears. Tried to tame that with Mullard 6DJ8s in the front. After I switched to the 5AS4s, I went back to Amrerex PW 6922s. Lovely sound. More natural, not fatiguing. The Mullard 5AS4s look like fat EL34s. Tall and straight. I've since found some Australian tubes that appear to be the same construction. Have not listened to them yet; so I don't know if they sound the same. Good luck with your amp. My friend at Cary will be pleased with your choice.

current tubes: USA Amperex 'pinched waist' 6922s; Sylvania 6SN7GTBs, FAA issue ca 1969; GEC KT-88s; Mullard 5AS4s.
Thanks for the fantastically comprehensive response! I'm looking forward to experimenting in the days and weeks ahead. Tell your friend at Cary that I'm in love with the amp.
I used Mullard GZ37's with very favourable results.
I have a great pair of sylvania 5u4's that I simply don't use anymore. They will crush anything russian made. I'll trade you for a cd of your choice. I like expanding my horizons....