The most common thickness used by production gate makers is 1 ½” thick material. They do this for several reasons. Mostly because it is quite a bit cheaper than 2 ¼” material, and because you can get it at most any lumber yard with out needing to mill it any further.
At Williams Gate Works, I hand select large beams and mill them to our specifications. 2 ¼” material is more stable for an outside gate that may face ever-changing weather. It will have far less chance of warping, cupping or splitting. It also has a much more solid feel to it. Like the difference between a 1 3/8” hollow core door vs. a 1 ¾” solid core door in your home. There really is no comparison.