Why are cavalry units so slow and weak?

[Titus Marcellus Scato]

What battle difficulty level are you playing on?

If you're new to EB, you might have chosen VH (Very Hard) battle difficulty, if you're used to that in stock RTW. But on that setting, the enemy units get +7 to attack, defence and morale. (Not counting the extra morale bonuses from AI generals with many command stars.) VH battle setting can make even weak slingers fight like elite units, and elite units become almost invincible. Suggest you try M (Medium) battle difficulty - that way the AI gets no bonuses other than morale gained from general's command stars.

Regarding charge bonus for cavalry, you don't get that when fighting slingers and other skirmishers, because they try to run away rather than standing still to meet your charge like normal infantry do (unless they are already bogged down in melee with another unit.) Fighting infantry in melee, you should use alt-right click on them to make your heavy cavalry switch to their secondary weapon (mace or sword). And don't leave your cavalry in melee too long - FM bodyguards especially.

Some heavy cavalry units have great stats but only normal stamina. Once tired or exhausted, they become far less effective in melee, and also move very slowly. Fresh, fast moving light infantry can easily outrun exhausted heavy cavalry. Another factor is that most pre-CE horses were only as large as modern ponies.

Generally, heavy cavalry work best against the flanks or rear of heavy infantry that are already pinned down in melee with friendly infantry. For chasing light skirmishers, use fast-moving light or medium cavalry that can catch them.