My son lives with a room mate. He works and his room mate is a student. Can they both claim their portion of the rent, and if not who is better off claiming it?

Which province are you in?

He lives in Manitoba

As per the Manitoba government:

Where a rental unit is occupied in a shared accommodation arrangement, only one
person may claim the Tax Credit. The lease or rental agreement must include the name
of the person claiming the tax credit. Furthermore, if one tenant in a dwelling unit has
received RentAid benefits from the Department of Family Services and Labour, only that
tenants can claim the Tax Credit. A tenant is not eligible for the Education Property Tax
Credit if the rental unit is in a single dwelling home occupied by the owner.

Thank you. Is it better for the working room mate or the student room mate to claim it?

It's a refundable tax credit, so both of them can benefit. The working roommate is more likely to have taxes owing, so they would have less tax to pay, while the student would likely just get it added to their refund.