The biggest difference is dosage. They are both primary glucocortoid steroids, and both do the same thing. They have different potencies, and many doctors find dosing and weaning easier based on different potencies.
The comparative potency is based on a standard of Cortisol being rated as 1 (one)...this is chemically the same as the steroid produced in our adrenals, so as close to biologic as possible. The differences are indeed caused by the way each drug is broken down or metabolized by the body, resulting in different "bioavailability".
Prednisone has a potency rating of 3.5 to 5, and Methylprednisolone has a potency rating of 5 to 7.5, so basically (using formulas I can never remember) 5 mg of Prednisone approximates 4 mg of Methylprednisolone.
The duration of action of Methylprednisolone is also slightly longer than that of Prednisone, 18 to 40 hours, compared to 16 to 36 hours.
As with any medication, "which helps the most" is highly individual, and it might be worth a try to see if it does help you more.