Playing at 100+ ping on EUW to 50 on NA makes the game *sooo* much easier. I just want to take the time to thank Riot again for moving the servers to Chicago. It's something a lot of us take for granted and it can't be understated how much better it feels.
With that said, the mechanics on NA are much worse than on EUW. Yes, I'm able to dodge skillshots a lot easier on NA simply due to ping. No, everyone else shouldn't have a harder time dodging my skillshots on NA. One thing that always annoys me switching between servers is the general attitude of players. NA is waaay more sensitive than EUW. On EUW we'll rage at each other hard, then apologize in post game like it ain't no thang. I was recently reported on NA for saying, "Wow, I did more damage than the mid laner" in post game chat and other innocuous things. NA players need to grow up and grow some balls.
Furthermore the playstyles and meta are different. On NA you can count on your team to follow up or generally watch your back even if you're doing something stupid. On EUW it's every man for himself. Supports would rather preserve their KDA than save their ADC more than half the time. Which I think is the reason why EUW has better mechanics. The game is more individualistic and requires better solo ability to win games.