I'd like to preface the main content of this post with the following: I understand this question may be equally suited to the Physics Stack Exchange, and so I have posted on there as well, but maybe a network engineer or computer science wizard may also be able to provide some illuminating knowledge.
Which medium allows for lower latency in data transfer, copper or fiber?
It is a tie (sort of). The transfer of information through electromagnetic waves, or the signal, has a velocity of approximately 200,000 km/s in both copper and glass.
A couple key advantages to optical transmission are it is immune to electromagnetic interference, and it has a much larger bandwidth, over 1000 times more than electrical transmission.
However, to achieve the lowest possible latency in a network, fiber should be used from the provider's equipment to the customer's network. Copper should be used from the customer's gateway to devices requiring a low-latency connection.
If the latency is the same in both mediums, then why not use just one medium, say copper?
The reason for this is that the distance from the customer's network to the telco's equipment is usually large enough that if the link was copper, it would require a signal repeater at some point to ensure the signal doesn't become too weak for the telco's equipment to register. Because of the additional device, the signal repeater, that data has to go through, it will take longer for the data to reach its destination than if it had traveled through just fiber. Optical transmission of data through fiber allows for much farther transmission of data due to the signal remaining stronger for longer without the need for a signal repeater to be used anywhere close to the amount needed in long distance electrical transmission (I think one would be needed for approximately every 300' in copper, but single-mode fiber can carry a signal for miles before needing to be repeated).
The reason why copper should be used in LANs is that many devices cannot yet work directly with light. Upon an optical signal entering a device, it has to be converted into an electrical signal. The opposite is true for a signal exiting a device. These conversions add time to the process. The points of conversion are essentially additional devices where the signal must pass through and be processed.