Great question to raise. It’s a tough one to answer because there doesn’t appear to be a definitive answer. There is not a lot of evidence pointing to whether they should be done together, separately, or if that even matters.
Instead, it’s best to focus on the type of grass you have, e.g. cool season or warm season grass. This way you can make sure if you go with one or the other, or both you are doing it at the right time of the year. Whichever you decide, doing it at the right time of the season will prevent damage to your yard and lead to a healthy looking lawn.
This is just a suggestion but I would start with aerating because the process will break up the thatch.
I hope this helps.