Companions are certainly the best. I think the charge does work, I've had my general caught out attempting to melee a charging enemy general, and I noticed he came off worse. The only problem with Companions is that you need a Royal Stable to get them and that can make campaigning annoying. If you're in deepest Germany or farthest Spain, you won't find many royal stables around there. So you can't use them aggressively without taking losses. For this reason I pack a lot of Macedonian Cavalry (okay, subject to the same restrictions in Barbarian lands but commonly available elsewhere), 3 of those and just the 1 Companion. I should also say that I've modded the game to give the Companions 2 hit points, which I've done just because I intend only to take the one and I think it's unfair that they die so easily. They're Companions for God's sake - cut me a deep hole in the enemy line!

Companions are the most powerful. However as ShieldWall already pointed out you can't retrain them a lot so any losses they take won't be replenished for a long time. Macedonian cavalry are less powerful but more retrainable, although you still can't retrain them in barbarian towns.

If you value retrainability and low cost Light Lancers are one of the best cavalry units in the game. They aren't too good in prolonged melee fighting but their high charge bonus (9, the same as Companions get) more than makes up for this.

The Light Lancers are an excellent value... some of the best cheap cavalry in the entire game, if not the best.

But I generally stick with the Macedonian Cavalry for doing most of the work because they're almost as good as the Companions and the wages are very reasonable. Their armor is good, but it doesn't weigh them down like cataphract armor.
I do, however, like to have one group of 54 Companions in my armies to help my general kill enemy generals. The Macedonian Cavalry can be your general use cavalry, and the Companions can make the decisive strikes.

Yes Lancers are good if the fighting is going to be very brief, otherwise they'll take a lot of hits. All cavalry work best in combination I think, rather than one unit charging on its own. So you get one to charge and another to hit it from the side or rear at the same time. Do this with light lancers and a rout should ensue - nobody likes getting that charge bonus from both ends at once!

Is it just me or is Cavalry on Cavalry fighting on VH/VH useless? I can have huge numerical superiority but I always lose serious numbers at least.

VH is just dumb, the AI gets hugely unrealistic unit bonuses.

But Cav skirmishes are generally unavoidable. I mean, it's either that or the enemy Cav ramming into your infantry rear.

As I see it, the only reason for not using companions is impatience. Yeah, okay, light lancers are good too, but companions are better. Just wait, take your time, build up yor cities...
And never ever go to Germania before there are minor cities there if you are playing as Macedon! First take over Greece, then Italy, then Asia Minor, then the Middle East and Egypt. Germania should be a very low priority. Who even mentioned it?

However, as I understand it, the charge bonus in the game does not work.

In early versions of the game, there was a charge bug but it was fixed at some point (not sure which patch). Make sure you have 1.5 or 1.6 if you have Barbarian Invasion and the charge will work.

Companions have the best stats, but depending on the specific battle, Greek Cavalry and/or Light Lancers can also be excellent horse units.