I have no personal experience with them, but I would assume so. Unarmored cavalry seems to have one speed, and armored cavalry another. I'm on turn 150 of a Turkish campaign in which I have solely used Turkomans (unarmored) and Sipahis (armored). The Sipahi description states that they have sacrificed some speed and mobility compared to their unarmored counterparts, but they are much better equipped to fight in melee for longer periods. I've certainly noticed this many times in my campaign-when the enemy army is sufficiently weakened by missile fire and it's time to mass-charge them, Turkomans close much faster than Sipahis. It's also noticeable when they're being chased by enemy cavalry.

So yes, they really are faster. I would say that unless you need to flee an enemy or really maximize your captures at the end of a battle, heavy cavalry is better. The speed difference is pretty slight, and so heavy cavalry will be able to chase routers almost as well. It's also important to mention that while harassment is a decent strategy, it's used more often because light cavalry must fill the place of insufficient numbers of heavy cavalry, and harassment is all light cavalry can really do.