I have absoluteblack oval rings on my hardtail and the inner ring on my road bike.
I have found (might just be in my head) that it is harder to get on top of/get in the sweetspot for a gear with the oval rings, but once you are on top of that gear, it is easier to stay there, especially when climbing.
There is a theory that oval rings reduce rear suspension bob on full sus mtbs.
Isnât the idea of a 55T chainring to keep the chain in the middle of the cassette more? 
Yes. But these guys have a straight chainline until they put the 55t on and they are now up at the top of the cassette!!!
I donât know what, if any, benefits there are to oval chainrings on road but for me they are a no-brainer off-road.
None of us have perfect pedalling technique so the oval ring helps smooth that out, circling the square if you like. This manifests itself as more even power applied at the tyre contact area so on loose ground you donât spin out as often and on snow you wouldnât be digging the back wheel in. I was out in 15cm deep snow at the weekend and could keep pedalling for much longer than my companions, well until I ran into 30cm drifts!
If you ride up a road climb on an MTB with knobbly tyres then you can hear the difference: rather than a rhythmic âthrumm, thrumm, thrummâ as you pedal you get a near constant sound coming back from the tyre.
Chain retention: no worse or better than a round chainring but I use a 1x drivetrain with narrow-wide chainrings and get zero dropped chains even with chains that have done 3000km. In fact the NW chainring on my fat bike is missing a tooth (clumsy airport baggage handlers) and still doesnât drop the chain.
OP - there was another thread recently about oval chainrings that might be worth reading.
I would never not run one on a mountain bike. Much better traction on loose stuff and Iâve never dropped a chain. Pros donât run them because they arent sponsored by them. Pros arenât paid to win races, theyâre paid to be a billboard.
Iâve never dropped a chain on my MTB either and I donât loose traction with my normal chainring. If oval chainrings were superior Iâd see them at amateur races, but I rarely do. Oval chainrings may be beneficial to some with a certain pedal stroke, but Iâd imagine itâs marginal at best. If itâs helped you then great, but I wouldnât recommend it as cure all.
As I stressed in my earlier post, they are a no-brainer off-road for me, sample of n=1, etc. but most, and I stress most, of those I know whoâve tried them prefer them to round chainrings. Maybe snake oil, maybe not but these are all people like me whoâve paid money for both and could switch back should they so desire but donât.
I wouldnât say the benefits are something obvious like 10% better, itâs subtler than that, maybe 2-5%, just enough to notice but not something that slaps you in the face. Iâm not someone who notices things like a 10mm difference in stem length that others scream about it completely changing the handling of the bike but I do notice this.
What is the supposed mechanism of better traction? I just ordered an oval ring for my XC bike, really just to try it out, not expecting massive differences
A more even application of power throughout the pedal stroke is what Iâm led to believe. Whatever the mechanics, it does seem to work (for me).
Not discounting the results or experience, but has anyone (chainring builders, or better⌠independent testing sites) actually shown data on this improved power application?
Not seen any, certainly not independent testing, like I said: âwhat Iâm led to believeâ.
So ⌠a bit of research, well Googling, came up with this piece - https://gearjunkie.com/oval-bike-chainring-review in which thereâs links to a couple of papers. Unfortunately both link to the same one, the conclusion of that one shows no benefit - http://ro.ecu.edu.au/cgi/viewcontent.cgi?article=7377&context=ecuworks - or at least small benefits that vary between individuals. The other paper was meant to show an improvement but since the link is broken Iâve not, yet, found it.
The next result on Google was this - https://bikefitadviser.com/oval-chainrings/ where he assesses four studies. His takeaway about oval rings is, youâve guessed it: it depends. He quotes parts of the conclusion of each study at the foot of the piece. Interesting the last has this:
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.
Which sort of describes my rather large legs 
Though heâs not currently very popular on the TR forum due to another video, his video on oval chainrings is interesting:
Do Q-rings improve power? Here is our answer, focusing on scientific facts and evidence not speculation. Yes here at FFT we have used q-rings & osymetric for over a year. However absolute proof they help is not clear. Here we talk about the basics of the effect of non-round (oval) rings on power, torque, pedal speed, bike speed. Firstly from a lab perspective where we can test one leg at a time, then in the field two legs. Thus we address: what exactly is the âdead spotâ in the pedaling motion? In the lab it is the effort the carry the leg back up to the 12oclock position, in the field it is the transition between the dominant downstrokes. Perhaps oval cranks work because of biomechanical comfort for some, perceived mechanical advantage for others. However we suggest to take into account the exact chainring size when deciding what ring is best for you. (rotor Q ring, osymmetric, doval, absolute black, ogival, one up, woolf, biopace). BTW if you were hoping for a simple âone-size fits allâ answerâŚyou will be disappointed. Non-round chainrings work for some people, sometimes for comfort, sometimes for pedal action, sometimes for power. For others they donât. In the opinion of FFT benefits on power are mainly because of the benefit of finding more appropriate gearing/gear ratios. However benefits in comfort may be seen.
Theyâre the same price as a round ring, so why not just try it and decide for yourself? Other than off road traction I donât feel any difference at all.
Lots of reports of poor front shifting and chain dropping. And an artificial 1-2% inflation in power readings. Thatâs the cons to non-circular chainrings that I keep reading.