You want me to refute your objectively wrong opinions by posting my personal opinions about 13? Sure. 13 has the best graphics out of any RPG released up to and at the same time it came out. It also has the most engaging combat of any FF game up until that point. The method of character progression in 13 is heads and tails better than any FF outside of 3/5/10/12, but that's not saying much because either there's no maleable progression in other games or they are retarded like 8's. Lightning, even if overused and part of the retarded story, is a vastly cooler designed/interesting character than any character in 8. Or in 1,2,3,5, for that matter.
Memorable moments? Lightning on the train. All of Pulse. When Shiva enters the picture. The storyline of Oerba, and the fact that the giant desert surrounding it is made up of the shattered bodies of failed l'cie. The Titan on Pulse. Fang and Vanille turning into Ragnarok (even though the reasoning behind it was retarded). Sera turning into a crystal just as Snow gets to her.
Those were all cool things about 13, in my opinion. The two cool things about 8 were Triple Triad, and Odin getting raped trying to cut Seifer in half. Everything else about 8 was bad, in my opinion.
However, in the world of "not an opinion," 8 and 13 are by far the most derided games in the FF franchise. Like, no other game even comes within several magnitudes of how much those two games are shat upon by the masses. I think 13 is a better game than many of the previous FFs, but that is an opinion. You think 8 is better than 13 and other games, and that is also an opinion. Admit that your opinion is not the majority, because I know mine isn't either. Hence, those two games deserve to be lumped together when offering them as a suggestion to other people to play.