OK I've run some simulations using a 1m diameter loop at 0.1, 0.5 and 5m above average ground.
The loop at these low heights in terms of wavelength is a high angle radiator with the peak of the pattern vertically upwards.
Mounted 0.1m above ground the pattern at a vertical angle of 10 degrees suitable for DX working is 13 dB below the maximum. The mounting heights of 0.5 and 5m are even worse with the pattern at 10 degrees 15 dB below the peak.
The conventional small loop antenna is not really a good DX antenna on 160m as it will pick up a lot of high angle interference and noise. It's main purpose is the reduction in local RF noise in many situations.
I ran a simulation of the cardioid loop antenna mounted at 0.5m above ground. This gave the peak in the pattern at 30 degrees. The pattern at 10 degrees is only 3 dB below the peak at 30 degrees. It also had good directivity so noise and interference off the back and sides of the antenna will be much reduced. The pattern is similar to a short Beverage antenna.
The cardioid loop antenna is relatively inefficient on 160m so it will give a lower level output to the antenna amplifier but with the high levels of natural background noise on 160m it is still very effective and will be far better for 160m DX than a simple loop antenna.