Methylprednisolone is stronger than prednisone:

Prednisone is four times as potent as cortisol, a steroid hormone that is present in the body. Methylprednisolone is five times as potent as cortisol.

I took prednisone for PMR. It decreased my immunity to infections but not to the extent that I had no immunity.

Both methylprednisolone and prednisone belong to the class of medicines called corticosteroids. They are synthetic versions of the hormone cortisol. One of the functions of cortisol in the body is to "regulate the immune response" in order to decrease inflammation.

Since corticosteroids are more powerful than cortisol ---yes, they do lower our immune response to infections. Our immune system is suppressed more but not completely eliminated. We are more susceptible to having an infection that may last longer. Nevertheless, we are not left without any defense against an infection.

The medication we take is a trade-off to controlling excessive amounts of inflammation. Some people say we have an "over-reactive immune system" that needs to be suppressed.