Using Verizon with my phone

I recently went into AT&T and they told me that right off the bat I could not use Verizon phone with AT&T service. I have previously done this in the past so I know that that is a lie they were about to close and I'm assuming that they just didn't want to help me . The phone I'm trying to use is a prepaid Verizon phone Stylo 2V the model is VS835. I've read several forums stating that I can use it. The SIM card in my LG G4 is a little bit too big so I'm assuming it's a nano SIM that is used is this correct please if you could confirm I could use? Thanks so much.