If I have two homes of equal value ($300K each) and one is paid off and other has a mortgage balance of $235K. I'd like to rent one of those out. Which one should give me the most advantages with respect to taxes and the value of money?
Which one should I take advantage of taxes and value of money?
If you have enough deductions to meet or exceed the standard deduction without the mortgage interest then there's no difference. If you need mortgage interest to justify itemizing or wouldn't itemize even with mortgage interest, then most likely the mortgaged property should become the rental.
For a rental, mortgage interest reduces your taxable rental income, for a personal property mortgage interest only helps if you itemize, and it only helps to the extent that it pushes your itemized deductions above the standard deduction. It's very common for people to only benefit from a fraction of their mortgage interest when itemizing.
One big caveat to the above could be if you intend to take the 20% pass-through deduction on your rental income. That deduction could shift the scales in some scenarios. This also assumes the property tax is equivalent, that HOA fees are either non-existent or equivalent, and that both would rent for the same amount. Any of those things could change the decision.