The fact that the style of the Quran and hadiths is different from each other proves that the Quran is the word of Allah.

The person who brought the Quran from Allah and the person who conveyed it to us is the same person, our Prophet Muhammad (pbuh). The Quran came from him and hadiths came from him, too.

However, if attention is paid, it will be seen that there is a big difference between the divine words that the Prophet (pbuh) conveyed as the Quran and the hadiths that belong to him. 

One does not have to be a scholar in order to understand this difference. Those who compare the style of the Quran and that of the hadith will easily see that there is an obvious difference between them. 

If the Quran were the words of a human being as those who deny it claim, the style of the hadiths of the Prophet and that of the hadiths would have to be different.

However, the fact that the style of the Quran does not resemble that of the hadiths and that the statements of the Quran are superior to all statements show that the Quran is not the word of the Prophet but the word of Allah, who made him a prophet and revealed the Quran to him.