Mortgage rental property or primary residence?

[Bryan Johnson]

In the simplest case of an investor with a single primary residence and a single rental property, where one of the properties is owned free and clear, and the other is mortgaged, in terms of tax benefits, does it matter which property is mortgaged?  If so, why?  I'm assuming house values and mortgage rates on either property are identical, equity is more than 30% on mortgaged property, and mortgage is under the $1M IRS limit for primary residence deduction in this hypothetical case.