Chris Froome uses some sort of eccentric, asymmetric chainrings -- dunno if he still uses Osymetric, which appears closer to Biopace than oval, with squashed, squared off ends. Team Sky/Ineos has always been pretty tight lipped about specifics regarding their marginal gains approach, and Froome is a savvy guy who, in interviews, only acknowledges that he likes the non-round rings, but I've never heard him share any specifics about how they know it offers some advantage.
And you know Sky/Ineos have measured, quantified and calibrated every possible thing to the nth degree. So unless Froome simply means he likes them because it feels right, and Sky/Ineos just go along with that to keep him happy, it's likely there is some measurable advantage... at least with him. It would be interesting to see some power data for both feet/pedals but I doubt that will ever be made available while he's still an active racer.
Froome has almost always appeared ungainly and awkward on bikes (other than time trials where he looks pretty smooth when he's not crashing). That includes his pedaling stroke, which looks kinda choppy even at higher cadence (compared with, say, Phil Gaimon, who's pretty smooth at high cadence). So maybe that's the key to why some folks like eccentric chainrings and others don't -- how smooth or ragged their cadence, whether we're pedaling circles or squares.
I don't have a power meter, let alone something to measure both legs and full stroke. Those cost more than all my bikes put together -- I'm such a cheapskate, I've never spent more than $200 on a bike. So I have no way of measuring whether I'm getting any benefit from Biopace. But it feels right once I have it tweaked to my liking (and today's 26 mile ride with lots of headwind was a good test). And I definitely have a choppy pedaling style, alternating effort depending on how my lower back, hips and legs feel. Sometimes I put more effort into the right foot, sometimes the left. With the Biopace rings it feels a bit more even than with round rings.
The Elevate browser extension for Strava shows that over the past three years my climbing speed has improved a bit, particularly last year when I mostly rode the old Trek 5900 with Biopace rings and 170 cranks. And I'm pretty close to that on heavier Ironman with the same crankset.
But it's all very subjective. I'm just gonna go by feel. If my knees are happy, I'm happy.
It has piqued my interest in trying a newer non-round chainring. I might check the various online discounters, see if they have something in my budget (like, $50 or less -- I did say I'm a cheapskate), and give it a try on a new-to-me bike build with a Diamondback Podium frame. It came with a nice Ultegra crankset but I'm not sure I'll get along with the 175 cranks.