To some extent it does overlaps and the UDLD functionality can cause a port to move into errdisable mode. Especially if you are working on SFP or GBICs i would suggest to go ahead with UDLD as well.
For more info do refer this link
Function of errdisable:
If the configuration shows a port to be enabled, but software on the switch detects an error situation on the port, the software shuts down that port. In other words, the port is automatically disabled by the switch operating system software because of an error condition that is encountered on the port.
When a port is error disabled, it is effectively shut down and no traffic is sent or received on that port. The port LED is set to the color orange
UDLD is a Layer 2 protocol that works with Layer 1 mechanisms to determine the physical status of a link. At Layer 1, autonegotiation takes care of physical signaling and fault detection. UDLD performs tasks that autonegotiation cannot perform, such as detecting the identities of neighbors and shutting down misconnected ports. When you enable both autonegotiation and UDLD, Layer 1 and 2 detections work together to prevent physical and logical unidirectional connections and the malfunctioning of other protocols.
Therefore UDLD is definitely recommended
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