Is cavalry best used to attack archers or flank infantry?

Both

Most logical army compositions will consist of more than one cavalry - there is no need to charge your entire cavalry into a single combat zone. Use light/shock against archers: light since they can quickly reach the archers, reducing the amount of volleys you have to suffer before forcing them into melee; or shock, which can kill/route weak archers very quickly. Heavy can either break their infantry ranks (leaving them easier to kill) or flank them to break their morale.

If they have more archer units than you do cavalry, you can charge your cavalry through one archer group into the other, resulting in both being engaged in melee and unable to shoot until they are repositioned. Most archers have very loose ranks which shock cavalry can easily charge through into the next unit.

Or Go for Archers

In the case where you only have a single unit or too few to charge both I suggest going for archers, since too few cavalry charging into the flank of infantry will not do enough damage/shock to break the enemy. However even a very small amount of cavalry can route high tier archers, which will also damage the morale of the enemy troops overall.

Unless they can run

But there is one exception which is your enemy fielding cavalry archers instead of foot archers. However light/strong your calvary is, the chase required to cut down their archers will buy their line too much time. In that case it will be better to just endure a few arrows and crush their ranks, forcing them to route. Even so, use your infantry to lure their archers to fire into your line instead of your calvary, so that after their line routes you'd still have cavalry to chase down their archers.

Whatever causes you more trouble, although charging archers is safer.

The best use for cavalry is to charge either from side or the rear at the vulnerable unit. But the "charge" is the key here - after the charge as cavalry you get a big damage bonus (equal to charge bonus) lasting for (I believe - please someone correct me) about 30 seconds.

To maximize it, you have to keep breaking the contact and commencing the charge again - and here lies the problem: infantry units might not let you break the combat easily and kept chasing retreating cavalry, which of course you can counter by escaping further away (so you'll have time to regroup and charge again), but that requires more micromanagement and puts more "downtime" on your cavalry usage.

In case of archers the risk is smaller, because they are much weaker in melee, so it is quite probable that they will rout shortly after charge.

This question depend on what enemy have best, archers or infantry. If you are fighting versus elves, you wanna pick faster archers before they destroy you with that so many range. On the other hand, if you are fighting versus dwarfs, is better to charge their infantry before they charge you.

For my experience, I prefer to charge archers quickly from behind, shattered them and then charge infantry from behind while they are moving to you.

The most basic way to look at units is to consider them as two categories: the frontlines and the auxiliary units (flanks, archers, artillery).

There is no one objective answer, it all depends on your enemy's army composition. This is by design, it keeps the game interesting.

If your frontline has the upper hand on your enemy's frontline, then you don't need to help them any further. What you want to do here is prevent your enemy from supporting their frontline, which you do by harassing their auxiliary units. For your question specifically, you would charge at the archers.

If your frontline is weaker than the enemy's frontline, then you need to support it. This can be done many ways (archers, artillery), but the "hammer and anvil" approach of charging the enemy frontline in the back with your cavarly is also a very effective option. For your question specifically, charge at the infantry.

Note: don't charge at anti-large infantry (usually spearmen) as they have obvious benefits against cavalry.

These are just two examples based on your question; there are many more strategies available. But it's not a clear cut answer, it depends on both you and your enemy's army composition.

Personally, I tend to have 2-3 cavalry units in an army, and I use them to harass the enemy. There are times where I don't have them always engage archers, but by moving towards them, you force them to retreat and thus waste time where they're not firing. It may lead to heavy casualties in your cavalry units, but this buys your frontline (with your archers) time to demolish your enemy's frontline (who now have no archers).

If I leave them engaged for too long they take heavy losses and flee.

Most cavalry should be used as shock cavalry: you charge in, do some damage, then you cycle back out and charge in again. There are many benefits to this:

• Shock cavalry tends to lack armor and/or melee defense, which means they're going to do badly in a prolonged engagement.
• Shock cavalry relies on their charge bonus, which only applies when you charge in, not in prolonged engagements
• Archers have lower accuracy against moving targets, thus keeping your cavalry safer (but not necessarily safe) from enemy missiles. In order to minimize being hit by arrows, try to move your cavalry perpendicular to the archers' firing direction.

You can, for example, charge your cavaly to the infantry, and then to the archer, and back (rinse and repeat). However, running straight towards archers makes it easier for your cavalry to be hit, keep this in mind.