I echo the comments made about the individual who wrote that. Not someone who is in any way an expert in my view (maybe an expert in self-promotion).
I have written quite a few posts about this, but I'll summarize some basics here...
1 - When I trained at Omega for servicing the co-axial, they made it absolutely clear that the purpose of the co-axial was not related to accuracy, but only to extended service intervals. This is not my opinion, but Omega's official position.
2 - If I look at the Swiss lever watches that I get in for service, very few (if any) are there only because of a lubrication fault in the escapement. There is much more to a watch than just the escapement, and therefore much more to maintain that just the escapement. In my view this calls into question the validity of the extended service interval argument. For those who say "yes but they extended the warranty to 4 years" and call that proof, you have to ask the question - could they have extended the warranty on their Swiss lever watches the same? IMO the answer is yes.
So does extending the warranty for your co-axial watches to a time period that is still within the recommended 5 year service interval of your older Swiss lever escapement watches really stretching the envelope in a big way? I don't think so.
As I've said before, if you want an escapement that is truly lubrication free, the Sinn Diapal system does that, and it's a Swiss lever watch.
3 - It's difficult to make any direct comparisons to other movements to be honest, but I service a lot of 2500 based watches, and even more 1120 based watches. These are the two movements that are closest to each other for the sake of comparison. Even though the 2500's have a free sprung balance and the co-axial, they are not any more accurate than the 1120 based watches in my experience. I base this on positional variation of the movements, and using the equipment I have on hand, which is designed for watch servicing, not in depth research. But these are practical measurements that directly impact how accurate a watch is in daily use, so are valid in terms of what people will see wearing a watch day to day. All can be brought in below the specs that Omega sets out for them pretty easily - remember the accuracy tolerances from Omega are the same regardless of the co-axial escapement or not, at least for now.
I have serviced co-axial watches that have ran with quartz like accuracy after I'm done with them, but I have also serviced all kinds of other Swiss lever watches that have been just as accurate. I've said it before, but if I had to pick the movement that I service that is on average the most accurate, it would be practically any ETA 7750 based movement. Even in non-COSC grades they are just very accurate watches, or can be made very accurate with not a lot of work.
The claims of "better stability over time" that have been made about the co-axial at various times are so vague I'm not even sure what that means. Stability of what? Balance amplitude? Rate? Beat error? And over what "time" is this increased stability supposed to be over? A minute...week...month...decade? Without specifics it's difficult to even know what claim is being made, let alone be able to determine if it's real...
4 - Beat rate in practical terms has little to do with how accurate any given watch is. There are some advantages to a higher beat rate, primarily rate recovery after a disturbance to the balance wheel, but even lower beat 18,000 watches can be very accurate. If I recall correctly 18,000 is what George Daniels originally wanted the co-axial watches to run at (don't quote me on that one though...). Also keep in mind there are co-axial movements that do beat at 28,800, so the 3313 does, and the 3201, 3203, 3330, 3603, 3621... and I could go on but anyway you get the point. Saying "Co-axial bad because of 25,200!" as the article does completely ignores the watches that are co-axial and run at 28,800.
5 - Where real accuracy gains have been made is with the silicon balance spring. Being able to form a perfectly profiled spring, and have it maintain it's shape is a big thing for accuracy. The "author" of that article says there is no difference between a parachrome spring and a silicon spring. Well sorry that's just pure BS. As I have said before, while at the Omega training I took a silicon spring and stretched it out into a straight line, and when I let it back down it went right back to it's original shape - no metal spring will recover like this. While the parachrome spring offers a lot of resistance to magnetic fields, it does not compare to the silicon spring in terms of being able to maintain it's shape.
So what does all this mean? If you like the watch, but it. If you don't, buy something else.
Hope this helps.
Cheers, Al