Well the trick is f.e. to use a spy and check how his cities are guarded, and strike fast when you see a weak spot. Sometimes the time you need to move the slower units would be too long to do that, and if you have some high produciton cities loosing a few horses isn't such a big deal. For the AI, seeing one of his best cities burned to the ground is a big deal thou
Just today i play Deity with Toku and Cathy as neigbours. Toku the backwards guy that eveyone hates due to no open borders etc declares war on Cathy.
He doesn't like me either as i refused to give him tribute, and i had a great spy that saw Kyoto is only guarded by 3 units atm with some close but moving away, and his mainforce in Cathys land.
So i took 7 or 8 horse archers and burned his capitol that was near me to the ground.
So let me just make sure I got this right you are claiming that burning a BC cap on Diety is a GOOD idea? And not just anyone, but Toko? HAHAHAHAHAHAHAHA.
Look, on deity when you burn a city the AI will just rebuild it and it will become a pain in the ass again in about 15 turns. Given the AI bonuses, the HAs you lose (let's assume 2) means that you come out BEHIND; even worse when you consider all the

you just burnt that did nothing relative to the OTHER AIs.
You might burn a city that early to destroy wonders you can't hold, but we are talking Toko, if he has wonders (which is rare) he doesn't do dick with them. You might also burn the AP as a matter of "damn I'm tired of being dicked over by these votes". But just because you can? Massively

inefficient move. Of course you are talking about running around with 7-8 HAs on deity and not taking masses of cities as a general rule you are doing something wrong.
You are bragging about pissing off an AI and likely lose more turns worth of production in so doing that Toko loses in rebuilding the city
Look the reason people don't like knights is the numbers. A HA fights 3 vs 4 with a spear even up, but that is rarely the case. Due to the XP advantage of the stable vs nothing more than the rax for the spear, the HA gets a free promo and CI/Shock is decent odds. At knights this advantage no longer exists, CII pikes vs Shock knights is not so forgiving. Likewise HAs will hit CG I(II for pro) archers. While archers do have an extra +25% for city defense; the HA vs Archer comparison is innately stronger than the knight vs LB comparison. Adding in CGII (III for pro) makes it a meat grinder for the knights. For even more fun, on low difficulties HAs can hit with 0 cultural defenses outside of the cap. On higher difficulties you are looking at 20% in most cities (minus maybe Cre civs) and 40% in the others. At knights everything will have at least 40% from culture and there will be huge numbers of castles.
Now compare to curis. Curis counter is ... still the pike. Castles ... are ignored. The top defender is typically going to be ... still a LB (muskets lose the +25% and don't have the 1st strike which I believe the AI still counts for top defender selection even though it is useless; plus the AI has to build muskets while it has masses of left over archery units).
But curis are deeper into the tech tree. Well yes, however guilds is a bastard tech. The AI loves to research it (so you can't trade it or the prereqs as widely). It isn't on a good bulb path (GE are the hardest to get and some of the most attractive to use in other fashions), and it doesn't go a lot of places (banking and econ are again AI favoured techs). In contrast curis come off of mil trad and gunpowder. Mil trad comes from music - which the AI never researches once the GA is gone, but will trade good techs to get - and nat - one of the most reliable lib techs you can get (which also let's you build the Taj for a GA so you can pound out curis quick once you get gunpowder). Gunpowder comes off edu (GS bulb which follows a GS bulb tech) - which is an extremely accessible tech that the AI delays and likes to trade. Also, this feeds into a lib push which can net you something expensive for free (like Nat or maybe even Mil Trad).
In closing, Casi, this is the strategy and tips forum. It is meant to be, shockingly, a place where strategy and tips are debated. If you say "knights rock" people want to know the strategy behind that so they can pick up a few tips to improve their game play. If you want a less rigourous response to your posts, I'd suggest you check out another forum. If you post here people will assume you want to discuss the finer points of strategy and ask you to elucidate your claims so they can either follow your lead or decide it is not the strategy for them.