“It seems like if someone has funds to pay off either their primary or rental, it would make more sense to pay off the rental first and keep the mortgage on primary, which would have the lower interest rate. Regarding taxes, I don’t think it matters which deduction you take (schedule A or C)”
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1. If rates are similar, I think that it is much better to pay down balance on primary first. Can make a big difference.
2. Various factors go into qualifying for an investment property loan. In many cases it is only .25% higher for this, but there is ALWAYS an option to pay up front an get the same rate as owner occupied.(With at least 25% equity, paying 1.75% of loan amount gets you same rate as OO)
3. Many people convert their primary into a rental and have owner occupied financing in place.

There are many strategies to use that may not seem like a big deal up front but have a huge impact on the bottom line over many years.