I am looking to install a pair of gates on 2' x 2' block (filled with rebar and concrete) pillars. Each gate panel is about 13' high x 6' wide and weighs about 850 pounds.

One gate company indicated that the footings should be 6' x 6' x 4' deep while another indicated 3' x 3' x 3' deep.

Does anyone know the proper size footings to hold the weight of the gates?

Your best bet would be contact the manufacture who makes the gate for the footing specs.

It kind of depends on the soil. I'm not a structural engineer but I work with many and the best ones over-compensate. I'd say go with the 6'x6'x4'deep!