It doesn't compare to Lake Michigan, which is more like an ocean than a lake.
I've raced my 16, 17 and Tiger in 7 - 9 foot waves on that lake. People go surfing on it - in the winter when the waves are even bigger.
Conditions like that would take any of the Island kayaks and crumple them up like matchsticks.
Here's what it looked like a couple of weeks ago in Grand Haven:
The "Islands" sail just fine in the Great Lakes.
The original question was from a person who hasn't got any sailing experience. I've been out in Lake Ontario in 6 foot waves, and both my boat, and I are fine. In fact, it was fun!
Looking at your picture, it doesn't matter what boat you have, a new sailor should not be out in those conditions. (and I don't see any boats around, so maybe the experienced sailors understand that fact too). When you say that "in the winter the waves are even bigger" you're right, but there aren't many new sailors who are going to go out on the Great Lakes in the winter. Let's be real. The Great Lakes are perfectly suitable for most Hobie products. I live on one, and was able to sail my AI the entire summer with very few exceptions.
Sometimes there's a bit of elitism on these boards when it comes to the Adventure Island and Tandem Island. We all understand they're different then a Cat, but let's not act like they're not Hobie's. They're great boats for certain users, and in my case, a perfect boat for a new sailor.