If every single thing was identical then they would probably alternate. But the problem is Google has so many signals, and lots that probably nobody knows about, that you will more likely find one ranks in front every time and you just wont know why. Could just be the way the content is worded, something in the domain name, or any other very small variable.
In this case, if we ignore everything outbound (links, signals, etc.)
I would say, usability, bounce back rate, on page time and user behavior would be crucial.
They won't be identical, because their content will be different. Whichever will have more suitable densities and better written stuff according to Google will be higher. No way to tell in advance.
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