Just to be clear from the start; the following text is only my opinion based on my experience with British motorcycles, and i am always willing to discuss my claims. I love Brit bikes in general more than any single marque.
However, as far as twins are concerned, my favourite is the home market Royal Enfield Interceptor Series II - but for ease of argument I'll leave these out. I shall also keep my discussion limited to postwar parallel twins.
In my opinion the Triumph twins - particularly the later pre-units - were generally the easiest on the eye, although special mention should be made of the BSA Rocket Goldstar. Commandos are a waste of space, but the Slimline Dominators are certainly a very appealing motorcycle. Ive never much liked the AMC twins, even the G45 is somewhat lacking
For rideability first place goes to Featherbed Nortons (of course) followed closely by Pre-unit, swingarm BSAs. Triumphs, commandos, 'hybrid' nortons (n15, p11 etc), AMC and unit BSAs have always been comparitively sub-par, although the duplex bonnies were above average.
Mechanically I swing to BSA for the more reliable, higher quality engines, with an honourable mention to pre-commando Norton motors, but AMC the last of the four major marques. The saving grace for the Triumph twin is it's versatiliy, due in main to the use of two camshafts instead of the single unit on BSA/Norton/AMC - and ive always had a very high opinion of the Daytona T100 engien
Ironically of course, the most technically advanced of the English postwar twins was the Sunbeam; OHC, shaft drive and so on, but i've never had much to do with them, so i cant comment.
That's very much the 'readers digest' version of my view, and as has already been said there are so many Pros and cons for each individual bike and manufacturer. singles are in a world of their own, and then there's the three and four cylinder bikes which we all know and love.
Anyway, in conclusion, I'll always favour those Series II Interceptors.