Plato believed that concepts had a universal form, an ideal form, which leads to his idealistic philosophy. Aristotle believed that universal forms were not necessarily attached to each object or concept, and that each instance of an object or a concept had to be analyzed on its own. This viewpoint leads to Aristotelian Empiricism. For Plato, thought experiments and reasoning would be enough to "prove" a concept or establish the qualities of an object, but Aristotle dismissed this in favor of direct observation and experience.
In logic, Plato was more inclined to use inductive reasoning, whereas Aristotle used deductive reasoning. The syllogism, a basic unit of logic (if A = B, and B = C, then A = C), was developed by Aristotle.
Both Aristotle and Plato believed thoughts were superior to the senses. However, whereas Plato believed the senses could fool a person, Aristotle stated that the senses were needed in order to properly determine reality.
An example of this difference is the allegory of the cave, created by Plato. To him, the world was like a cave, and a person would only see shadows cast from the outside light, so the only reality would be thoughts. To the Aristotelian method, the obvious solution is to walk out of the cave and experience what is casting light and shadows directly, rather than relying solely on indirect or internal experiences.