Aside from the obvious differences in the physical connectors, is there an advantage to one over the other?
Specifically, I am looking to connect powered near-field monitor speakers to my USB audio interface.
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XLR connectors have a lock, so they are less likely to be unplugged by accident. Also, when connecting or disconnecting them, they are less likely to cause short circuit or produce noise because of their design (the TRS design may cause that). In general, the connector is more robust.
In your scenario, check if your monitors and interface support balanced signals, and if they support it, you can use a XLR cable that will carry the "control" signal on the third wire and will protect your signal from interference. If you use a TRS connector, be sure to use a three-conductor TRS connector to carry a balanced signal.