Cuirassers seem to be just a slight improvement over Knights -- they have a bit higher strength and an innate withdrawal chance. But if you have Cuirassers, you're only one tech away (Rifling) from Cavalry, so you might as well just keep going.
Have another look at the tech tree; once you have Cuirassers, you're still
several techs away from Cavalry.
Military Tradition and Gunpowder enable Cuirassers. You tech there from Philosophy and Civil Service through Nationalism, and Music is a pre-req. Rifling is on a very different branch of the tree, teching from Civil Service (or Theology) through Paper to Printing Press, Replaceable Parts, and
then Rifling, with Banking thrown in as a pre-req along the way (for RP). I usually have Cuirassers many, many turns before Cavalry or Riflemen are available. I'm coming to really like the unit, especially as they don't really have an effective counter until Riflemen show up.
I'm also finding not all of the BtS AIs are as in love with Rifling as their vanilla and Warlords predecessors. Willem, for example, seems to prioritize naval techs such as Astronomy and Chemistry over the Rifling path.
Speaking of Cavalry, can anyone tell me what the big deal is? They are countered by Riflemen, which the AI loves to fill up its cities with. This would lead me to expect that the big city-attacking unit would be Grenadiers, but that doesn't seem to be the case.
As with many things in Civ, the big deal isn't getting there, it's getting there
first. If you get to Cavalry first--or at least before whomsoever you wish to inflict them upon--you have a unit that at strength 15 is stronger than any other unit around, and it has 2 moves as well. It will stand up to counter attacks and absorb damage in a stack before other units that have other jobs to do (such as your precious city raiders); it will chase down and punish any would-be pillagers; and build enough of them and they are quite sufficient at taking cities--and holding on to them. No, they don't fortify or earn defensive bonuses, but it's often possible to both take a city with half a dozen to a dozen Cavalry and then move them in to defend the city on the same turn.
Just because Riflemen show up it doesn't mean that the Cavalry's day is done. Have you ever attacked Cavalry in the open field with low-promotion Rifles? The odds aren't overwhelming--usually in the low 70% range. The AI is often reluctant to attack with those odds unless it has a large number of units to throw at you. And the AI doesn't upgrade many of its units, so there can still be other defenders against whom your Cavalry are still effective.
Grendadiers used to be wonderful city-takers in vanilla and Warlords, since you could tech to them faster than you could to Rifles, and all your CR-promoted melee units can be upgraded to them. And with their bonus against Rifles, you could still field them against the AI's favoured defender of that era. Their only counter was--wait for it--Cavalry. In BtS, however, the availability of Grens has been pushed back in the interest of balance. I usually don't bother with them now, preferring to tech to Rifling before going after Military Science, since a very handy production tech (Replaceable Parts) is along the way and it now enables two top-grade units (Riflemen and Cavalry) rather than the 2 mid-grade ones enabled by MS (Grenadiers and Ships of the Line). And frankly, when I'm close to MS (after Chemistry is done), Steel is a much more tempting tech, for Cannons and the Ironworks.
Almost certain to withdraw seems to be too hard to believe.
I'd have to agree. With Flanking II, my withdrawal odds are rarely above 50%, let alone getting near 100%.
It's better to think of early mounted units with Flanking promotions as early Catapult substitutes. They don't do collateral damage, but they'll damage a defender and there's a slight chance that they might survive the attack to fight again.
Their super escape rate when upgraded properly (the extra %escape from level 2 and 3, then the move speed at lvl 4 and sentry at lvl 5). Having a large army of these can be great due to this escapepercentage - use them as defensive strikeunits based in bordercities. Offensive, well, I like axe/swordrushes better.
(you can get it reasonably early enough to make a huge impact still since the AI's tend to tech slower now)
