I don't know if JAA FI is the same in Sweden and other European countries, but I actually believe it is.
Yes, from my experience it's a very big difference between a JAA and FAA checkride. I personally think JAA is better. JAA focus more on the basic stuff, straight & level, climbs, descents, turns etc. but also things like slow flight, steep turns, navigation and traffic pattern. FAA focuses more on certain maneuvers like Chandelles, Lazy 8, Lost Procedure & Diversion and all different types of landings.
During my CFI I was grilled for 8 hours during the oral part, on my FI the examiner almost forgot that I should lead a lesson in meteorology (ended up being 30 min). I think JAA FI was both easier and gave me more from an instructor point of view. But different requirements for JAA and FAA certificates require different requirements for instructor ratings.
Please note that everything I write is based on a Swedish JAA FI.