RE: Brimar vs. Mullard, it really depends on the exact tube types you are comparing. Both generally have the warm British sound.
As I've mentioned the triple mica black plate Brimar are wonderful tubes.
Many like the Mullard M8162.
You can find some great Mullard 2-Mica CV4024 for about $25-30 each if you're diligent. Great tubes for the money. Later production (early 80's) is what you're most likely going to bump into as NOS tubes, but again, great value.
If you want something more geeky, rarer, altogether better, look for late 1950's Mullard Whyteleafe CV4024. Most folks are familiar with the Mullard Mitcham and Blackburn plants, but they had another one at Whyteleafe that just made superb tubes. Their factory symbol is a square with a line drawn diagonally through it. The 12AT7 produced there are exceptional. All of the normal characteristics of Mullards, beautiful mid-range, silky smooth highs, but also vey tight, disciplined control of the bass which is particularly unusual for Mullard tubes. The Mullard 10M 12AT7 is another nice one. I have some Mullard E81CC/6201 but they honestly haven't done too much for me. Valvo E81CC are better. Siemens, too.
Another delightful rarity are the early 1950s Philips Copenhagen 12AT7/CV455, etc. Very rare. But exceptional quality. These are often misidentified as Philips Herleen tubes because both plants use a triangle as their mark, but the triangles are different. If you pay attention to that you can scoop up some EXTREMELY valuable Philips Copenhagen Welded Plate 12AU7/12AX7 for a $100 or so when they are worth $1K+ because someone thought they were Amperex tubes.
If you wanna get geeky with your 12AT7, look into 7062 and E180CC. There are some very nice pinched waist examples of both out there.
Good hunting.

