I really enjoy my first experiences with both, but I have 2 problems, actually 1 need of advice and 1 disappointment...
1 I was beaten by a slight margin by the AI in.... SJ tutorial 3. I am not really used to lose a tutorial

It seems I have a problem here:
how can I defeat a shock army (japanese) with a missile army (chinese/corean)? If veterans have advices for me, I would gladly hear it.
And it would be also useful for P&S, I started the campaign with the turcs, and I feel that I have more or less the same kind of problem, my troops seem to be weaker in melee than my foe.
2 there's one thing in the game mechanics that I find really questionnable:
most infantry can't charge a horse, that I understand.
But that infantry can't join a melee already under way, creates weird situations: that an infantry, not engaged or threatened by anyone, is not able to support a friendly unit being attacked by cavalry, and watches it being slaughtered under its nose for several turns...
Even if it can't engage the enemy cavalry, it should be able to do something to help it. I don't know, giving a bonus to its ally, or forcing the cavalry to fall back from the melee.
Or anything.
But a situation where cavalry butchers with impunity a unit, while being itself surrounded by tons of infantry which can do nothing at all, and that for turns after turns if the melee lasts... It feels really wrong to me.