What's the difference between light and heavy cavalry?

[Whiskers of Sheogorath]

It costs the same ammount of upkeep funds, though heavies are being a bit longer to produce. What's the difference between those two? Like, one is a swag horse and other is not?

[Lemurian1972]

Not sure where you're seeing they have the same upkeep. It depends on which specific units you're comparing. Generally speaking though Heavy cav units are more expensive, but it depends on which era the unit comes from.

The biggest difference comes in the promotion trees. The second is in the timing of when you get access to each. Light Cav units are designed to use high mobility to help main units get flanking, and for pillaging. Heavy Cav are designed to stand in, take some punishment, and beat stuff up, as well as hammer on cities.

[Exemplar]

Different promotion paths is the main difference. Light get bonuses against siege units, bonus for flanking and pillaging. Heavy are stronger offense against fortified units and districts, can eventually gain multiple attacks where movement allows.

[gimmethegepgun]

Another thing to note is that the normal heavy cavalry units other than the Knight get +1 movement if they start in open terrain, and a lower base movement to compensate (which is part of the reason why the Knight is so completely brokenly OP).