I’ve come to realize that a lot of what I would consider to be the best scenes in anime cannot stand alone, or at least have a difficult time doing so. They require prior knowledge of everything that has happened beforehand and to have proper empathy for the characters on-screen.
The best scenes are payoff, and this is often why when one shows their favorite anime scenes to someone unfamiliar with the show, it won’t have nearly the impact.
There are exceptions of course. My favorite being the following scene from Macross.
Misa: Your baby’s so cute! May I hold her?
Miria: I made this baby. If you want to hold a baby, go make your own.
I guess it’s better to say that dramatic moments are better with context.
OGIUE MANIAX 
I think payoff scenes are better than scenes that work well out of context. Out of context scenes are usually regulated to one-off jokes (like the Misa/Miria quote you provided, which IS awesome, but I still say “Catch!” was funnier) and don’t have the same emotional impact that a payoff scene has.
And I think, really, that in any medium, scenes have to be taken in context to understand the impact they have. It’s like reading a Wodehouse book, and you’re sorely tempted to read that hilarious line you just read out loud to someone else but there’s absolutely no way you can do it without whoever has to listen to you staring at you and going “why is that funny?”. Same thing with Susanna Clarke books.
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