For AA upgrades:

from US to Europe - you can either upgrade by 10FF (10000 miles for one-way upgrade if it's Full Fare), or by 25SS (25000 miles for one-way upgrade for most economy fare).

Go to aa.com, click on AAdvantage, then Partner & Mileage Program, then airline, then click American Airlines.

You may also want to do a search under "upgrade" under each of the airlines you are considering for information.