For a LONG time now Quicktime has had an issue exporting to H.264 where it'll bump up the gamma and make your exports look brighter than it did originally. It's a long-standing bug that I'm fairly shocked hasn't been addressed yet.
A simple-ish fix is to install x264encoder from here. It's FREE.
After installing it, re-launch your export software and select "x264Encoder" from the export options and before anything else, hit the Options… in the lower left.
From there hit "Tagging".
At the top left checkmark "Add gamma 2.2 (SD/HD content)".
This will dramatically fix or at least help the gamma H.264 shifting problem.
x264encoder seems complicated but since there are some really great presets you can get amazing results, small files sizes with only a few clicks. Exports will take longer to encode though sometimes so be aware.
A great article on this is here which goes into much more detail.
For curiosity a deprecated method (in case you don't have x264 installed or have don't a connection on location) is here. x264encoder is something you should have on that flash drive in your pocket, btw.
Thanks to IK for reminding me I never posted this after mentioning it ages ago.