Possible refinance

I’m on an ARM with a current interest rate of 3%. I spoke to a lady from Churchill Mortgage yesterday and I can get a 15-year fixed at about $1070. My current payment is $805. So that’s a big jump, comparatively. My other alternative would be to get a 30-year with a payment of about $740. The lady said that if I got the 30-year, I could always pay more. But I know the tendency is NOT to do that, so I’m leaning towards stretching to make the 15-year payment. Opinions, suggestions?