To express the thought "I warn you", you can either say "je vous préviens" or "je vous avertis". The basic meaning is the same. Hold in mind that: 1. "Prévenir" has other meanings that "avertir" doesn't. It can namely mean "to prevent". Mieux vaut prévenir que guérir. Prevention is better than cure. 2. "Prévenir" tends to be used for a friendly warning, while "avertir" tends to be used for threats. L'élève a reçu un avertissement : s'il désobéit encore une fois, il sera puni. The pupil got a warning : if he disbehaves once more, he'll be punished. Mon ami m'avait prévenu : je n'aurais pas dû boire tant d'alcool ! My friend had warned me : I shouldn't have drunk so much alcohol !

From an ethimologic point of view pre / viens means before you come. It is a friendly advise before you move. For Avertir, think about the CARTON JAUNE ,JELLOW in the game of soccer; If you continue, you will have the CARTON ROUGE, RED. Avertir is much less friendly, it means you will get punished