Firstly, the cost of getting to or from your normal place of work is NOT a deductible expense in Ontario. Unless you can show that you use that transit pass for travelling to work OTHER THAN to and from your normal place of work, you can't claim it.
Who deducts the cost of travel in other circumstances depends on who pays it. If the corporation pays, the corporation deducts. I believe that if the company pays your transport costs then that counts as part of your salary and you would pay tax on it (the company can consider it an expense).
EDIT: As Chris Rea points out, there is a tax credit for transit passes (which can be claimed no matter why you bought them). It's a personal tax credit only, so you have to have bought them and you claim the credit. Whether you are a contractor or an employee or unemployed makes no difference.