This site http://www.frontiernet.net/~jadale/Loop.htm states that: "A
properly designed Loop primarily responds to the magnetic component of the
radio wave. Note that noise resides primarily in the electrical
component..."

Whereas this site shows that that is not the case:
http://vk1od.net/antenna/shieldedloop.

So what is the advantage, if any, of a shielded loop antanna?

Consider three receivers:

1) Shielded loop antenna, receiver with differential input (center-tapped
transformer or instrumentation amp). The two ends of the inner conductor
of the antenna connected to the differential inputs and the shield
connected to ground.

2) Same as above but without the shield.

3) Unshielded loop antenna, receiver with single-ended input.
One end of the loop connected to the receiver input and the other to
ground.

Assuming equal gains and bandwidths, would there be any
difference in the sensitivity or noise level at the output of the three
receivers?