Depends
Most likely, only one would lose power. That totally depends upon the cause of the outage and where the problem is.
With separate feeds (two source points coming to island) and only one is interrupted, then the other line is good and still providing power. You could be out while next door has power if fed from different source.
Could be close as local transformer on the island going out. Past the transformer (downstream) is out but just the other side is still working as that is (upstream) before the problem.
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