Thank you both for these appreciably detailed answers!

I have read them both thoroughly, and discovered what I guessed was true; that Vices and Virtues screen makes a very large difference.
I am now considering using assassins more often.

However - what strange fortune - I have made a triumph just after creating this thread!
Beginning an Early campaign as the Aragonese in XL 3.0 with Tyberius 2.0, I conquered in my most difficult battles - Europeans vs Arabs! As I wrote in another thread here, I formed a great alliance against the Arabs, and in many battles defeated them with a kill ratio of 5:1.

In one of these, I had 1 Feudal Sgt., 3 Spears, 3 Archers, 1 Javelins, 1 Urban Militia, and the Prince against;

5 Ghulam Bodyguards, 4 Ghulam Cavalry, 2 Camel Archers.

Into the woods I went! And the Khaliph himself came riding in with his four sons, after they tried to barrage the army.
They were surrounded by the archers, who were backed by the spears, and as the arrows started the crossfire, the militia charged in amongst the bewildered enemy under a withering support of javelins.

I have never seen so many Ghulams dead in one forest! Although the Urban Militia were depleted to one quarter strength - I almost destroyed the entire Royal family!

Spears and javelins have become my main units in Iberia, though this may change if the Catholic Alliance falters in time.

As for match-ups, I ask if these are correct statements;

Valour being equal, Swords beat spears.
Spears beat cavalry.
Cavalry beat swords.
Ranged units are auxiliary with few exceptions.
Heavy cavalry beats light cavalry.
Beserkers are fun.