I don't wuite see how can a hill woth three crosses engage another hill with three crosses? XD

To elaborate, calvary is not the same as cavalry, though both are known for spears penetrating soft flesh. Okay, my minor amusement aside, let's talk about horses and lances.

Middle ages are a long, long period of time, and how Carolingian horsemen fought was somewhat different from how Agincourt-era knights did. My area of focus is high middle ages, so I'll stick to those.

First off, we recognize two general types of cavalry, heavy and light. These aren't necessarily divided by equipment they use, but by their tactical role - thing is, that tactical role requires certain equipment, so it's a bit of a chicken and the egg situation.

Heavy cavalry serves as a shock force - its purpose is to find a soft-ish spot in the enemy lines and punch through it, routing the enemy. This may be a flank, enemy wing with untrained or demoralized troops, anything really. Sometimes, you may deem enemy weak enough to attempt straight up frontal charge, problem is, if you're wrong about their capabilities and/or morale, you're going to, to use a technical term, get rekt.

Light cavalry on the toher hand serves a harassment role, it circles around the enemy, using its superior mobility to quickly strike at momentray weaknesses and withdraw away if threatened. It uses its speed to only fight when it has overwhelming advantage locally. It can't attempt an effective frontal charge aainst the line infantry (okay, it can, but it will only rarely succeed), but is great for taking out unguarded supply lines, archers who left themselves exposed, catapults, routing soldiers or any other target of opportunity.

Now, there is some overlap between the two, shock cavalry can certainly start harassing the enemy, thing is, it won't be as good at it as the light, and doing it will make it not be in position for that shock you want to break apart enemy lines.

With that in mind, cav on cav fights happened differently depending on light/heavy ratio.

When heavy cavalry is seeking to charge into enemy flank, it may well encounter enemy heavy cav trying to do the same. They are likely to charge each other, with the winner delivering the coveted flanking charge right into the poor, poor infantry. Sample battle: Marchfeld, 1278

When heavy cavalry looking for a flank encounters light cavalry, heavies have a problem. They're better at melee than light cav, but not so much better that they want them to charge them from behind once they themselves are done with their own charge. Ideally, heavy cavalry will use its own light cav force to screen them from enemy light cav (this screening force was very often made of squires of the knights themselves) and charge, if that is not viable, thay may have to decide to attack light cavalry. Light cavl that is competent will then withdraw, luring away the enemy heavy cav, essentially protecting their infantry from the charge. Sample battle: Grunwald, 1410

Light cavalry on light cavalry plays out just like heavy on heavy, only with more mobility, and usually with more willingness to withdraw, since light cav is there to harass and delay, not to fight it out in uncertain melees.

Now take these components, add to them healthy dose of chaos, massive pile of lack of good intel on both sides, plain old human stupidity, terrain and weather, and you have a rough draft of how things played out.

To specifically get to heavy on heavy charge in more detail - movies leave out thet those weren't that fatal, because armor is awesome, and shields even more so. Both men and horses of heavy cavalry were armored pretty heavily, and there are techniques you can use with the lance to not get hit by the opponent (shown for example in Fior di Battaglia, c. 1400). Lot of people still get killed (what with it being a war and all), but it's not a death sentence for all without plot armor. honestly, proper shields and helmets help...

Oh, and I forgot to mention that movies tend to not give people in them shields or helmets.