It really shouldn't matter which end you monitor, they both will show the same info albeit "back to front".
I generally monitor the remote device uplinks so that if that remote device gets removed, I don't have to do anything to my core's monitoring settings. But if it's only a single uplink to the remote device, then generally I don't monitor the interface at all as normally bandwidth between core and comms closet isn't an issue.
That's a good idea about monitoring the remote end so you don't have to change the monitoring on the core. That's definitely a plus. I did notice one caveat with only monitoring a single interface between two switches and that the L2 Network Topology information for the device shows it's connected to the remote node but doesn't show which remote interface or the speed of the link. This is nice to have readily available, but a description tag on the interface works just as well.
Thanks for the input!