If we look at this just from the point of an attacker, we have to take into consideration that not only is heavy cavalry weaker in attack when considering population, but it also costs much more.
It strongly depends on what you're focussing on. So let's say we focus on attack strenght per population, ressource cost per population, recruiting time per population and unit speed. We are ignoring the defense on purpose for now.
First, attack strength per population:
Light Cavalry has 130 Attack and needs 4 population, so 130/4 = 32.5 AS / pop.
Heavy Cavalry has 150 Attack and needs 6 population, so 150/6 = 25 AS / pop.
Light Cavalry ist 30% more effective when it comes to attack strength per population.
Cost per population:
Light Cavalry has a combined cost of 475 ressources and need 4 population, so 475 / 4 = 118.75 ressources / pop.
Heavy Cavalry has a combined cost of 950 ressources and needs 6 population, so 950 / 6 = 158.33 ressources / pop.
Light Cavalry is 33% more cost effective than Heavy Cavalry when it comes to ressources per population.
Recruiting time per population (Barracks 25):
Light Cavalry has a recruiting time of 5:40 and need 4 population, so 5:40 / 4 = 340s / 4 = 85s / pop.
Heavy Cavalry has a recruiting time of 8:38 and needs 6 population, so 8:38 / 6 = 518s / 6 = 86.3s / pop.
Light Cavalry is slighty more time effective (~1.5%) when it comes to recruiting time per population.
Now, last but not least, movement speed:
Light Cavalry has a movement speed of 8:00 minutes per tile.
Heavy Cavalry has a movement speed of 9:00 minutes per tile.
Light Cavalry is 12.5% faster than Heavy Cavalry.
Taking all these points into consideration, Heavy Cavalry is not that useful in attack, especially considering you get much more bang (+30%) for your buck (+33%) when using Light Cavalry. The minor speed improvement may actually also be of importance.
Please consider all these things do not take into consideration that Heavy Cavalry has strong defensive strength, much more than the Light Cavalry.
What you do with this data is up to you, including what you choose to do with your units. Enjoy!
