What Are The Best 12AT7's and 12AX7's?

Be careful with recommendations of one variant or another being the
"absolute best". For instance: "The best 12AX7 is a 5751,
the best 12AT7 is "variant XYZ", etc."

While it is true that a PARTICULAR BRAND/VINTAGE variant can be
better IN YOUR EQUIPMENT, there are a lot of poorly made and
mediocre sounding variants of many types of tubes. For example, many
tout the superiority of the 5751 in my EAR phone pre. While it is true that
the Sylvania and GE 5751's sound very good in it, IMO they don't compare
to the Telefunken 12AX7. And I have some 5751's by other manufacturers
that sound much worse than some very ordinary 12AX7's.

I have amperex bugle boy, telefunken ribbed plate , mullard long plate, cv4004, and telefunken ecc803s is the best for my equipment. No contest

There is a lot of varients,for both tube types mentioned for sure
The black plate RCA Command series is a standard of excellence against any company, also Sylvania Gold Series these are some of the best the US made, also a gt tube with a WA or JAN were military issue and allways doubled screened for noise. And there is no such thing as best for General Electric also makes the 5 star series also very good ,more of a neutral
Tube that is very well balanced the RCA is usually the warmest,with the Sylvania a bit cooler, the Black plates are the oldest and also a bit warmer then the 60s grey plate versions .then you have Phillips ,which owned
Amperex,and Mullard the SQ, And PQ are there better grade.there is
Many who like Siemens of Germany,if buying the Siemens ,Halsky is their older better tube earlier 60s,Telefunken with the Diamond in the glass
These have European numbers all very good every brand has it's own tonal balance . The tube that sounds best in your system is the best tube.
European tubes are much more $$ then US tubes.Amperex was made in NY for example their white labels are premium and have great detail and a little body - PQ, buy also made in Holland,and other factories.This is just a sample there are many good tubes out there
The rarer the tube the more money,also look for very close matched pairs
And have checked for low noise .enjoy your Valves as the Brits would say.

without getting into anything too exotic,ive had good results with the new tung sols and new mullards,,,however there is some great tubes now coming from canada