Which would be more eventful? Barbarossa survives to the Levant or doesn't go on Crusade?

Basically Barbarossa managed to achieve an unseen level of central authority and order to the Holy Roman Empire. Shortly after he proceeded to join the 3rd Crusade with a massive army. However unfortunately for him he would drown while crossing a river causing most of his army to return home.

What would have been more impact on the events of history though. Had Barbarossa lived would him remaining in Europe to strengthen his hold or going on Crusade with the King's of England and France have had a bigger effect on history and if so what and why?
 
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