Okay, this sounds much more likely to be on the same phase . . . but maybe you still want to check to be sure.
If they are indeed on the same phase, then the problem is likely to be caused by the ground resistance between the two circuits. Are they wired to two physically separate electrical boxes, or have you used any ground-isolated outlets or such? If this is the case, then the actual ground connection between the two circuits is at the electrical panel, and there's likely to be a few ohms of resistance between the ground connections at the plugs, which can cause significant ground currents to flow through you interconnects.
The best way to solve this would be to have both circuits brought into a single, metal multi-gang electrical box, and all the ground connections for the plugs and circuits be connected together inside. This will reduce the ground resistance between your circuits to a tiny fraction of an ohm, and should remain code-compliant.
Now, it's true that a properly designed balanced interconnection system should reject noise created by slight AC ground currents (common-mode), but it's been my experience that the presence of an XLR plug has little to do with whether or not the particular component was properly designed with common-mode noise rejection as a goal. And this is a very low-level hum you're talking about.
If they are indeed on the same phase, then the problem is likely to be caused by the ground resistance between the two circuits. Are they wired to two physically separate electrical boxes, or have you used any ground-isolated outlets or such? If this is the case, then the actual ground connection between the two circuits is at the electrical panel, and there's likely to be a few ohms of resistance between the ground connections at the plugs, which can cause significant ground currents to flow through you interconnects.
The best way to solve this would be to have both circuits brought into a single, metal multi-gang electrical box, and all the ground connections for the plugs and circuits be connected together inside. This will reduce the ground resistance between your circuits to a tiny fraction of an ohm, and should remain code-compliant.
Now, it's true that a properly designed balanced interconnection system should reject noise created by slight AC ground currents (common-mode), but it's been my experience that the presence of an XLR plug has little to do with whether or not the particular component was properly designed with common-mode noise rejection as a goal. And this is a very low-level hum you're talking about.