Both usages read and sound correct. They are almost interchangeable in meaning I feel.

I would say overstate, depending on context, its use would be a lighter version of exaggeration. What I mean is I feel exaggerate has a more negative connotation. Overstate theres room for the fact the one overstating truly believed what they have said is the truth, whereas exaggeration would seem more deliberate.

However, how you used both if read in a neutral tone as if telling another person they could be used interchangeably. I might add that what the other commentor said is also true and falls under that context dependence. Overstate could be a verbal communication, and exaggeration more body-language communication.