Is it permissible for an employee to take a percentage of the price difference between two contractors after saving the company money?

It is not permissible to take anything from the company without its knowledge. If you find a more competent contractor for a lower wage, inform your employer. If the officials agree to give you a bonus, there is no harm, otherwise, do not take anything without their knowledge. You are entrusted, and you must strive for what is best and deal with the most competent. Taking the difference between the contractors' wages is not permissible, based on the hadith of Urwa ibn al-Ja'd al-Bariqi; for the increase belongs to the principal, not to the agent.