I would say it's that Black has no trouble with developing and castling quickly, while after 1. e4 e5 white can play Nf3, then everything black does, white always seems to have some move that forces black to respond, and black ends up with a slightly more cramped defensive position. With the french exchange however both sides are open. However that doesn't mean the french exchange is EXACTLY equal.
I wouldn't always take literally pronouncements of "equality" even by GMs as they seem to get a kick out of doing that for openings they don't think much of. Nick de Firmian is a particularly egregious serial offender for this where he'll label any opening that doesn't see much GM play as "leads to equality with best play" when that really misses the whole point of openings. Every opening in the end "leads to equality with best play", that doesn't nullify the point of the openings.
GM Ben Finegold (https://youtu.be/4mI0UO1xklo?t=300), timestamped @5.00, mentions that after 1. e4 e6 2. d4 d5 3. exd4 exd4, black has equalised.
I do not understand how black has reached equality in this completely symmetrical position. If black has equalised there, then why is there 'no equality' after 1. e4 e5, or 1. d4 d5 ?
Moving away from this specific case, I find it hard to grasp the concept of 'gaining equality' for black - what does it mean, and what has to happen for it to occur?