"Try on" is widely used to mean "experimentar" (no sentido de "vestir/calçar"). So, generally used to refer to clothes/shoes.
"Try out" is used to in the sense of "experimentar" (testar), meaning "testar para ver se dá certo". So, one can try out a computer program, a policy, new ideas, an experiment (with experiment you can also translate it into "levar a cabo"). And try out other things as well.