どちらも「見返してやる」という意味合いですが
１）I will get you back.
「必ず[仕返し](https://eikaiwa.dmm.com/uknow/questions/71650/)してやる」的な[復讐](https://eikaiwa.dmm.com/uknow/questions/80869/)（revenge)の意味です。バカにされた相手に同じ目に合わせるという物理的に何かを相手に仕返しをするぞという感じ。
例：
Just wait. I will get you back.
「待ってろよ。必ず仕返ししてやる。」
２）I will prove them wrong.
「自分をバカにした奴らを、アッと言わせるような自分になって見返す」という自分がポジティブに変わって相手を後悔させたり、びっくりさせる決意も含んでいる感じの表現です。
Everybody thought that I couldn't become a fashion model, but I proved them wrong.
「周りのみんなは、お前がモデルになるなんて無理って思ってたけど、皆を見返してやった。（モデルとして活躍している）」
見返し・仕返しを意味する表現です。
使い方は以下の通りです：
例文：
John: Hey Julian, I heard that Dave wrote something strange on your facebook wall. （デイブがあなたのフェイスブックページに変な書き込みをしたと聞いたよ）
Julian: Yeah. Don't worry, I'll get him back.（ああ。気にすることないさ、仕返しするから）
ジュリアン
"You'll regret that." - This means that the person will be sorry that they made fun of you.
"Watch your back." - This implies that you will get the person back at a time that they least expect it so they should be on guard.
"I'll get you back." - This is a simple, direct way of letting the person know that you will repay him for what he did, possibly by making fun of him too.
"You'll regret that." -バカにしたことを後悔するだろう。＝見返してやると言う意味になります。
"Watch your back." ＝いつか思いもよらないタイミングで痛い目あわしてやるから見とけよ。と言う意味があります。
"I'll get you back." -これがシンプルで直接的に相手のやったことの仕返しを表す表現で、バカにしたことなども含まれます。
The two sentences you see provided above are great ways to express to your listener that you will get them back. In the second sentence you will notice a common saying. We use this to let our listener or listeners know that we will get back at them eventually. This is a common saying in English and is appropriate for informal settings.
1. You'll be laughing on the other side of your face.
2. You're so petty!
3. Do you want me to wipe that grin off your face?
1. This is a threat. This person is laughing now and this phrase means they will not be laughing later. You will do something. You are warning them.
2. This phrase just means that this person is immature and obsessed with trivial or unimportant things. There is no threat. It is a typical retort.
3. This implies that you may physically hit the speaker so as to stop him making fun of you. However, the level of aggression depends more on body language and the way the words are said than on the actual meaning of the words.
"You are going to pay for that" means that you going to do the same to them.
Instead of saying "I'll get you back" you can say " I will get back at you".
"You are going to pay for that"とは、同じことをすることを意味します。
"I'll get you back"または、" I will get back at you".と言うことができます。
"What comes around goes around" This is a Phrase that means if they do something bad to someone then something bad will happen to them.
"Karma will get you" Karma is an invisible force that does things to people who do bad to others.
"I will get them/you back" If you are speaking to the person you say "get you back" If you are speaking to a friend about the other people you say "get them back.
"You'll regret that" This means that you are going to do something so they will rethink what they did and wish they never did it.
"You will pay for that." Means that you will do something to them that is equally as bad or as funny to others.
"What comes around goes around"
巡り巡って自分に降り掛かってくるものだ
人に悪いことをすれば、悪いことが自分にも起こるという意味のフレーズです。
"Karma will get you"
悪いことをすると、いつかはツケが回ってくる
Karmaは、他人に悪いことをする人に起こる目に見えない力です。
例文
"I will get them/you back"
仕返しをしてやる
話している人にと言うのであれば"get you back"、友人に他人について言うのであれば、 "get them backと言います。
例文
"You'll regret that"
そのことを後悔するぞ。
あなたが仕返しをするつもりで、相手が自分がしたことを決してしなければ良かったと考え直すだろうということです。
例文
"You will pay for that."
ただじゃおかないぞ。
あなたが、相手にその人にとって同じくらい悪いことや変なことをするつもりだということです。
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