Although Mylene described all you need to know in a nutshell, i feel that maybe it's helpful if someone (in this case: me

) gets a little bit more into detail...
^^ Compare the needed techs. The goal should be to strike before the AIs are close to Rifling themselves.
Right after Lib, you can have Cuirassiers in many situations. It's a critical point: if you've managed to be ahead of the AI, the best units you might face are Knights/LBs/Muskets/Warelephants/Pikes, all of which you can handle very well with enough # of Cuirassiers. It's just right after Lib when you usually have the technological edge to be ahead of the AI, when you wait the AI era bonuses will kick in and they get better production with better workshops/windmills/watermills (AI relies alot less on whipping, so that's when they start to take off in production), alot better research with things like Free Market or Printing Press and so on ... If you do not use that edge right when it occurs, you might find yourself in a situation where you actually can't break out without one AI running away with the game.
When you go for Cannons/Rifles, it's much more likely you'll face a much bigger powerhouse. You'll face endless swarms of Cavalery flanking your cannons, you'll see Grenadiers taking out your Rifles, you'll see Airships weakening your top defenders and all the annoying bs like Privateers or maybe even Machine Guns (and you really don't want to face those with only Cannons/Rifles...).
OTOH, you're pretty save to avoid all that stuff with Cuirassiers. Long story short, they usually come in a timeframe when you're mostly facing Medieval units, while you're going on rampage with Renaissance units, while you can't gurantee that with Rifles/Cannons at all.
+ Curs (and later Cavs) just move much faster.
... and the faster you move and the faster you reach your target, the less time there is for the AI to send/whip reinforcements. You'll also be able to react to counterattacks more flexible, and your own reinforcements will be at the frontline alot faster. Less time needed for wars directly translates into less time for the AI to maybe reach key techs for either bribing someone else in or to finally field useful troops.
Ones in a while you might think about using Cannons with drafted Muskets; although that might work, when the AI decides to go for Cuirassiers itself you'll be flanked to death, i promise you that

OTOH, most of the direct Cuirassier-counterunits can be easily dealt with by promoting your units according to what you're facing. That's basicly impossible with Muskets/Cannons, no matter how many Pikes you'll bring along those cuirassiers will flank the livin' hell out of you.
Finally something Mylene didn't mention: 2-movement-units are way more elegant and fun than those slow-grinding cannons.
