Yesterday I replaced the left and right rear tail light assemblies in my e38 740iL. The right side was damaged in a crash and I replaced the left also so they'd match. Both sides brake, reverse, and turn signals are of equal brightness. The parking lights are not. The left parking lights are very bright, the ones on the right are not as bright. They were not like this before I replaced everything. What could be the problem and the solution?

I agree with Rich Sheffey to check for difference in bulbs. Even with the same part number, mistakes in manufacturing happen. Another possibility is that the reflector mirror coating inside the tailight lamps is different between sides. If both were purchased from BMW they should be the same but if they are not the same, the dimmer one should be replaceable under the parts warranty.
Your picture seems to show that the tailights on right has a red section in the center and the Left tailights are amber and white. Is that an illusion?
check the bulbs of the two that are different, swap sides, does it follow the bulb from the left to the right?