After your earlier thread on amplifiers and preamps it was great to see you have purchased the Ypsilon amps - they are excellent.
With regard to the SME 15A versus the 20/3 - the 20/3 is a decent step up in resolution, solidity, and sound staging. The 20/3 bridges the gap between the 20/2 and the 30/2. By comparison the 15A is an upgraded model 10.
from the HiFi+ review of the 15A
I have long been a fan of the SME 20/3 and, as it was to hand, I put the two up against one another to see how they differed. The four footed and pricier turntable with the mighty Model V arm delivers a more solid, assured, and three dimensional sound than its sibling. It produces more depth of image and greater resolution of reverb and harmonics, too. Essentially the character is the same, but you get more of the detail off the disc.
You have a very good system that deserves the 20/3 level of performance.
The 30/2 is up another notch but if you can buy a 20/3 new vs a 30/2 second hand I would be tempted to go with new, you never really know how tonearms have been handled, no matter how knowledgeable the owner, and bearings are easily damaged through mishandling.
Something to consider - if you put a reasonably priced good quality MC in the 20/3 you will get a better result than putting a more expensive cartridge in the cheaper deck.
By the way nobody answered your original question -
SME vs AMG vs Technics
SME has a sense of ease and grandeur - very smooth, excellent soundstaging, and quite transparent. If you are familiar with Spendor loudspeakers - the SME has similar qualities - very smooth, unforced presentation that allows you to listen into the music. Superb on classical. I have listened to the SME with a variety of cartridges - 2 of the best for me were the Soundsmith Paua and Van den Hug MC - both presenting great level of detail with musicality.
The AMG I have heard is very smooth, but I found the AMG with their own arm/cartridge underwhelming. Slow. I know someone here who replaced the AMG fairly quickly after purchasing due to lack of dynamics and energy.
The Technics - presents fairly lean and clean.
Of the 3 I would recommend the SME.
Others to check out would be the Brinkmann Balance and Kuzma M/4Point11.
The Kuzma which I have heard at length and fettled, is a very easy TT/arm to set up for folk that don't do TT set up often. The Brinkmann is a great deck - a legacy product. Some of the Brinkmann Balance owners prefer the Kuzma 4Point11 arm instead of the Brinkmann arm as a combo.
Best of luck.