I love theme parks and I think Everland is the best around Seoul. Everland is actually a group of parks and they manage Caribbean Bay, a waterpark. I haven't been to the others so I can't compare but the best time to go to Caribbean Bay in my opinion, is at the end of September, or anytime after Chuseok. If you go before, it will be way too crowded and you won't be able to enjoy anything. I was pretty disappointed the second time because there were so many people!
As for the rides, Everland is better than Lotte World. There is also less people around April/May, so it is very nice. The rides are more thrilling than at Lotte World, but still nothing super scary ^^ I only have a few pictures from Caribbean Bay.
They have super cool waterslides and it's too bad that we don't have this in France! If you go to Carribean Bay, even if there's a 4 hour wait, be sure to ride the Boomerang! :D