I'm looking at this, forstarters, from a tax point of view: if you have a mortgage then you can deduct "that" (= the non-principal components) from your rental income. This will reduce your overall tax bill. Depending on your individual tax bracket/rate this should save you money after all numbers are crunched, factoring in the amount of interest you pay as this is, obviously, a true cost.
This of course also means that you, during the phase of paying off these mortgages quickly, will have less cash in your account. So it depends - as always - on your individual needs and therefore situation.
And then there's the topic of using leverage - IF you plan on expanding your holding and/or otherwise want to invest. Because the less money you do not have "stuck" as equity in your properties the more money you can use to otherwise make money. Example: you pay off your mortgage (quickly). This leaves less money in your pocket to set aside and save for another down payment of a 3rd place which would generate more (positive) income.
Now, if you do not want to expand your holdings nor otherwise invest that money (e.g. stock market) then you may indeed want to pay off your mortgages more quickly as this will, ultimately, increase your cash flow afterwards significantly. But also your tax bill due to no longer having that part available as a deduction. Again, if you're in a low tax bracket this may not make that much of an impact. For others it certainly does. That is something only you can decide. You should probably run these scenarios by your CPA to see which makes more sense within the parameters of your needs.