I've found this. Is it accurate? IDK. But I'll put it here for arguments sake comparing a 2 element Delta and 3 element Delta vs a 4 element Yagi.
https://www.claw.deltaloop.it/en/delta-loop-vs-yagi/
DELTA LOOP VS YAGI
Ever since Loop antennas came out, the controversy that has most characterized the debate over which antenna is superior has mainly focused on the comparison between the two systems’ forward gain.
Even though Loop antennas, as fully shown, have a significantly higher gain compared to the homologous Yagi-Uda models, there are other features that make Loop antennas interesting and preferable.
Here are some noteworthy features.
GAIN
As an integration of the diagrams shown in
Why Delta Loop about the comparison between Loop and Yagi systems having the same number of elements and between Loops vs. Yagis with the same boom length, what follows is a diagram regarding the comparison of two different 14 MHz antennas, published on the ARRL Antenna Book, edition 21.
What has been made is the comparison of two streamlined models having the same boom length (ca. 8 metres) and different number of elements.
Notice, in particular, the larger number of elements on the Yagi-Uda model.
ELEVATION ANGLE vs. HEIGHT FROM THE GROUND
A Delta Loop and a Yagi antenna, placed at the same height from the ground, show a very different take off angle (elevation of the main lobe’s signal).
The smaller is the take off angle, the bigger is the distance of the bouncing RF signal transmitted by the antenna, the better are the chances to make QSO at higher distances.
The following diagrams show typical take off differences between Yagi-Uda and Delta Loop systems. Note that at 6 metres from the ground is found a difference of as many as 8° in favour of the Delta Loop. By using both diagrams it is possible to better analyse the importance of the elevation angle.
Credits: ARRL
HORIZONTAL/VERTICAL BEAMWIDTH @ -3dB
By comparing the typical beamwidth of a Yagi and Delta Loop system having the same forward gain, can be noticed that the -3dB beamwidth of a Delta Loop is basically wider than that of a Yagi-Uda.
This is a precious feature both for long distance DX and for competitions (i.e. Contests).
PRACTICAL COMPARISONS
The summary of the features that make an antenna more performing is shown in practise: situations in which all the intrinsic (antennas’ characteristics) and extrinsic (propagation modes, morphological site characteristics, etc.) variables occur, which are typical of all installations.
Here are some interesting studies carried out by practically testing (at the same time) compared antennas.
Ham radio Magazine – September 1978
Glenn William (N2GW) makes a 2 element Delta Loop 14 MHz, which he compares with a 3 element Yagi and a 2 element Quad.
Here are his conclusions:
Conclusion
The 2-element delta loop has been a real performer for me. It’s allowed me to compete in several DX pileups and comparefavorably with others using full-size 3-element Yagis and 2-element quads. Even after my linear was recently sidelined, I was still able to work out very nicely just using my exciter. Also, the low vswr allowed me to bypass my antenna tuner and still enjoy a vswr of less than 1.5:1 across the entire band.
QST – October 1966
Robert Fitz (W4RBZ) compares the two systems installed on two 25 metre tall towers, taking notes of the received signals.
The results represented in the chart show that in the 73% of the cases the Loop had the same or better performances then the compared Yagi.
QST – February 1971
John Parrot Jr. (W4GRU) compares 4 different Loop models with a 3 element Yagi.
His conclusions:
The antenna tests indicate that:
1) One can expect to achieve the same or better results with a two-element quad of proper dimensions than with a three or four element triband Yagi.
2) A wide-spaced quad will perform substantially better than a close-spaced quad.
3) Dollar for dollar, the quad appears to be a better investment than a Yagi.
It is intersting to observe that openings to the U.S. lasted 15 to 30 minutes longer on each end of the period than with the Yagi.