It depends on who you want to believe. Elliptical chainrings _do_ work for some people, but not everyone. Every rider has a somewhat different biomechanical efficiency. The elliptical chainrings may help, or even hurt depending on the individual. For the vast majority there isn't much of a difference.
Further to the point that your physiology is a major factor on the effectiveness,
https://pubmed.ncbi.nlm.nih.gov/16846753/ "The use of an eccentric chainring during an outdoor 1 km all-out cycling test" states:"when time was saved with the eccentric chainring, it was significantly correlated with estimated lower limb muscle volume.....The physical variables associated with eccentric chainring performance were muscle anthropometric parameters. We have interpreted our results cautiously and suggest that the subjects who had greater lower limb muscle volume and greater calf muscle volume, seem to have had a significant advantage in performing with the eccentric chainring."
But in general, there isn't much of an effect. Most studies find no benefit.
https://pubmed.ncbi.nlm.nih.gov/21266731/ "The influence of elliptical chainrings on 10 km cycling time trial performance "
From the abstract: "Elliptical chainrings do not appear to provide a performance benefit over traditional circular chainrings during a mid-distance time trial. "
https://pubmed.ncbi.nlm.nih.gov/12955523/ "Physiological responses during cycling with noncircular "Harmonic" and circular chainrings "
From the abstract: "comparison of the physiological response in this study did not translate into an advantage of the Harmonic over circular chainring during submaximal and maximal pedaling in trained cyclists. "
http://www.ijsei.com/papers/ijsei-88619-19.pdf "Optimally Positioned Elliptical Chainrings Show No
Performance or Physiological Effects in 30s Sprints"
From the conclusion:"elliptical chainrings benefited neither performance nor blood lactate production during 30s Wingate tests. "
Even a study sponsored by Q-Rings saw no overall benefit. from
https://triathlonmagazine.ca/training/bike/pedal-power-do-elliptical-chainrings-really-work/ "The study found no conclusive performance advantage to using Q-Rings, ...."
But, there are claims of success. Chris Froome, Bradley Wiggins, Magnus Backstedt, and Sara Storey have all won championships with them, and many professional riders (though a substantial minority) prefer them. I have a Wolf Tooth elliptical on my FS MTB. The only difference I can see is that it feels a little funny when I first get on the bike, but after a few minutes I don't notice.