The key to the two examples you gave is the difference in the Rate.
The APR is based on the Rate plus the Fees in APR.
The Est. Payment is based solely on the Rate.
So because the rate is significantly lower from NationsChoice, the APR and Est. Payment are both lower.
If NationsChoice’s fees were a lot higher than American, they could push the APR higher than American, but the Est. Payment would still be lower.
If anyone has any information/experience about the criteria necessary to obtain one of these loans, I would love to hear about it. I am wary of the companies that list mortgages on bankrate.