Same here

Thanks Bill...

I swapped sides with the same result. Could it be one assembly is slightly darker? Maybe from a different manufacturer?

If you have the parking lights on a dual filament bulb will get brighter when you apply the brakes because both filaments in each bulb will be lit. (Dual LED bulbs should work the same as regular dual bulbs.)
Did you try swapping the bulbs from left to right of the car - does the problem stay on the side of the car or move with the bulb.

(Google "jewish lightning" if you really want to know. Otherwise, it is Bill just being snarky.)

They get brighter when I press the brake. I replaced the filament bulbs with LED same result. 

If the problem bulbs are dual filament (as in the picture attached) there's a chance that one of them is in upside down. With this type of bulb, it should fit in only one way. The "bayonet' lugs on the sides are a different distance from the tip of the bulb. However, if the socket is worn or just on the loose side (tolerances are generally poor)  it is possible to get the bulb in the wrong way around. When this happens, the weaker filament, which is supposed to be for a tail or parking light gets the brake light power and glows weaker than the other brake light By the same logic, the stronger element gets the the tail light power and glows brighter than the other tail light.

If they are this type of bulb, turn on your parking lights, take out the brighter tail light, turn it 180 degrees and reinstall it. If the bulb is fully seated, you should not be able to turn it without pressing in on it a little.

Do both tail lights get brighter when you step on the brake? Was wondering if the one of the bulbs for the brake light was 'stuck on' on the right side.

They must have gone to private schools. That's weird though. Around here the left bulbs are way brighter than the dim bulbs on the right.

No, what’s that?

did you try jewish Lightning ?

I have a 2009 Mini S. The right side tail lights are brighter than the left. Changed all of the bulbs with no success, ground issue? Thoughts.