They should go over your medical history and previous cycles. When I got my 2nd opinion they also did a complete exam (pelvic exam, ultrasound, etc). After all of that we sat down with the RE, her nurse, the embryologist and the financial person to go over all of our options. With the RE and the embryologist we mainly discussed my 2 failed cycles and what each thought had gone wrong with them, based on the information they received from my first RE. They also gave me information on their lab, their thoughts on 3dt vs 5dt, and stuff like that.
The main question I would ask is, given your history why do they think your previous cycle(s) failed and what would they do differently. They should tell you these two things without having to ask - but that is really the bottom line in making your determination to switch.
As far as contradicting information - that is tough. I was lucky and had an idea in my head of what I thought my issues were and the 2nd opinion just confirmed it. I think your gut will tell you which one you feel is right. I loved my first RE but I knew I had to do something different if I was going to keep trying.
Getting a 2nd opinion gave me renewed energy and got my back in the right mindset to keep going. I hope it does that same for all of you. Good luck!