when fighting a creature that have strength 8 / craft 8 and winning, do you keep it as a trophy of strength if you fought him in battle (and craft if in psychic combat) (this is how we are playing now), or do you choose his type (strength/craft) when exchanging trophies?

You choose. (I don't remember at the moment but this might be written in the faq.)

I play Talisman Digital Edition (the computer game of Talisman). When you fight an enemy with both Strength and Craft and beat it, you can exchange it for either Strength or Craft. It does not matter if you beat him in battle (Strength) or combat (Craft).

You choose whether to trade it for Strength or Craft.

cheers all!