Both can be extremely cringe depending on how it's done.
Emo music is a lot different, the colors and the way they dress is usually different, emos definitely have distinct hair styles, etc. And emos usually cut their wrists open amd think they are depressed because their mom didn't buy the right kind of pizza rolls. (Based on a true story)
There are a lot of differences, i definitely prefer the gothic style, but it really depends on how it's done, because i looked it up, and everybody looked like they were trying to be vampires, and it was really cringe.