The two seek a reform of philosophy, in which knowledge can, guide the action.
With scientific study, Bacon wants man to find true principles. Recognizes the need for human reason to have additional tools that allow man to know nature and subdue it. It is necessary to combine experience (the senses) and understanding (reason) through induction based on the choice and elimination of particular cases, until we get to know the most general principles.
For Descartes, philosophy means the study of knowledge. Descartes created a method to demonstrate truths based on the needs and demands of his own reason.
Descartes defended the existence of only one knowledge, true and evident.
For him science is one, even when it has different branches ..
Descartes and Bacon agree on something and that there are hidden things and you have to discover them, Bacon names it through the forms and Descartes through doubt, because if we doubt we can find things that at first glance are not seen. The difference in your thoughts lies in the objective of knowing and in what we know. In the aim that for Bacon the goal is to achieve a new science made of those forms that were previously hidden but thanks to the method are discovered, while for Descartes the objective of knowing is to verify, man uses his reason in different ways but all guided in a trajectory, the certainty. The second difference is that for Bacon who decides things are things. For Descartes who decides is the Subject.