I'd say the opposite really. I think it's much harder as a long term fan since we were so use to being "the big guys" of the league, instead of the joke we are now. The hardest thing about it is knowing that we have the resources, and are very close to being one of the top clubs again but we're being held back by Wenger/the board. Not taking shots at LP but when I heard the suggestion of resigning Kim Kallstrom my heart sank because of how much the standard and expectation of the club has dropped.
I started watching Arsenal at a very young age so I've experienced 2 premier league titles, FA cup vs UTD and also the CL final vs Barca. Back then I was too young to actually analyse the football or gain enough knowledge but I still grew a strong bond towards the club, which is why I absolutely hate when people say "maybe I should support club X instead", even if they are joking.
Wenger needs to go and I've admitted that I'm part of the Wenger out brigade. But he's been the only manager I've experienced so when he does leave it'll be an emotional day.
For your question LP, I use to give France a strong following for the cups in 2004/2006, mainly because of Thierry/Pirez and Vierra