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I generally copy the style of the show, but loosely.
For instance, despite my heavy anime style, if it's a Western cartoon I don't turn the character into an anime, I use references of the original style and do whatever shapes I feel more comfortable with.
One thing you have to keep in mind is: it was designed to work in that particular style, so unless you're absolutely sure of what you're doing, changing the style might break the appeal the character has in the first place.
Also copying the face is more important than the body for keeping the original appeal, unless the body proportions are very particular to that character.
Pic related is from Google. Everyone looks generic and unappealing, the only reason someone would pay attention to this is because it has the clothes/colors of the iconic characters. None of the characters' traits were creatively adapted into anime form. Ok, arguably giving Plankton a hoodie, but that's about it.
