Boyfriend being rude to me and comparing me to another girl?

So im in a 3year relationship with him and most of the time its been very difficult between us. Over the past few years he has lied to me more times than I can count, talked to numerous other girls behind my back on a dating site and on fb (I later found out about this through his email account) flirting with them, calling them hot and beautiful and asking if they wanted to meet up with him. When I confronted him he denied everything and got so mad that he threatened to call the police if I didn't leave. I also have reason to believe he physically cheated on me. I broke up with him 4 months ago because of all these things and because he was always so rude to me. At the end I couldnt take it anymore I missed him so much and started texting him again, hoping he would have changed and take me back. At first he was very distant and rude telling me to leave him the hell alone and that he wasn't in love with me anymore. The next day he told me that these where lies and he still loved me and thought about me all the time and that he would change (tears and everything) So I took him back. He has now compared me to another girl in a fight (we where fighting because he falsely accused me of having sex with another guy) when we where broken up he used to hang out with this girl a lot, he also told me she tried to have sex with him and that they shared the same passions and goals and that she was his savior ( she apparantly helped him stop doing drugs, which I've tried a 1000 times without succes) this all made me very jealous. He compared me to her saying "at least I could talk to her, and she would listen to another opinion than her own" Im very hurt by this because I was always there for him, even if no one else was, listened to him and tried to help him every way possible. I dont know what to do anymore, should I stay with him or not? Sorry for the long post!
Boyfriend being rude to me and comparing me to another girl?
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