The way they worded the headline is a bit awkward but if you isolate it's clear they meant Canon "beats" Sony .. ie
"Canon dominates DSLRs, (and) tops Sony in mirrorless.
This is another tidbit. I looked for the numbers and could not find them ...
"Sony Takes Over As No.1 In U.S. Full-frame Cameras"
"As DSLRs fade into the history books of photography, Sony has emerged as the official leader in full-frame cameras in the US. Newly-released NPD data shows the remarkable growth Sony has achieved through a combination of innovative next-generation mirrorless cameras and a thriving community of active creators who are reimagining what photography and videography can be. "
https://alphauniverse.com/stories/sony-takes-over-as-no-1-in-u-s--full-frame-cameras--launches-historic--be-alpha--campaign/
As I mentioned, different market, and full-frame only. The sources are listed at the bottom - they come from a market research firm, not from Sony's own bragging.
The Canon vs Sony contest is shaping up to be a very interesting one, and it may have less to do with camera body technology than lens technology.
Very broadly, you can divide the (better-than-phone-camera) market into three groups - performance-seeking, price-limited and size/weight-limited. Obviously, there is overlap - you can be a performance-seeker, but be price- or size-limited away from medium format, for instance, but, broadly speaking, any piece of equipment will be more or less attractive to each group based on its characteristics.
Camera forums and high-end users tend to represent the 'performance-seeking' group. This is where the A7r3, D850, D5, fast supertele lenses, super-sharp f/1.4 and faster primes, not to mention medium format, belong - a zone where price represents little object and customers are willing to carry big, heavy lenses and backpacks full of gear to get the best possible shots. Canon and Sony are both highly competitive in this field. Right now, Sony probably has the advantage, since they have an established full-frame body lineup that improves markedly with each generation and a rapidly-expanding lens lineup, while Canon is still rooted in old SLR technology and needs to get its full-frame mirrorless system off the ground; this is not irreversible, though, since Canon is a large company with more than enough resources to chase and catch up, much as Sony did when it went from being mainly an electronics company to competing with Canon and Nikon for the camera market.
But it is with the other two groups, representing a far bigger market, that Canon may have an upper hand in the medium term - and it largely comes down to their lens technology, not their sensor or body technology.
Canon has invested a lot of effort into developing diffraction optics and other beyond-classical optics. This allows lenses to be made smaller, lighter and cheaper (once mass production and economies of scale come into it) than non-DO lenses. Initially, there was a performance deficit, with the 'onion ring' bokeh in early-generation DO lenses, but improved manufacturing techniques for more precise optical surfaces, particularly on the nano-scale (similar to what Sony initially advertised in its G Master series), has largely mitigated this, and continues to improve. When used, it allows Canon to make a smaller lens with the same optical characteristics (focal length, aperture and image circle), or a lens of the same size with wider aperture, longer focal length or covering a larger image circle.
It wasn't so long ago that Canon said that, in a few years' time, we'd have compact zoom lenses with a 10-1000mm focal length range. They didn't mean that this would happen using ordinary optics. What Canon's developments would allow is things such as a full-frame mirrorless camera, the size of a Leica M-series, with a range of small, compact zoom and prime lenses stretching from 16mm f/4 to 200/4 and beyond - essentially, a full-frame Olympus E-series M43 camera with much greater capability. A lot of people - particularly the travelling crowd - aren't willing to lug a D850 or A7r3 with 10kg of lenses around, but are more than happy to bring an Olympus E-series with two or three small lenses. Canon could one-up them, delivering much more capability in a package of the same size. Or, for the more budget-minded, optical developments would allow for a 1.6x crop camera with a 10-1000mm lens (angle of view similar to 16-1600mm on full-frame) in a relatively compact package, delivering similar utility to Nikon's P900, but with much better image quality (particularly in low light) due to the much larger sensor.
Sony has its RX series bodies, as well as a number of pancake-type lenses. But, without new optics - diffraction optics, optical metameterials, electroactive optical materials, etc. - they can't go much further than this. Sure, they can continually improve sensors and electronics, as they will always do, but they won't be able to make significantly faster or longer lenses without running into physical size or cost limits, let alone come close to matching the effective reach of 'compact' (to use the term loosely) cameras such as Nikon's P900 and P1000, whose 24-2000mm or 24-3000mm equivalent angles of view really provide the imprimatur for their existence (their 1/2.3" sensors being otherwise low-end even by compact camera standards).
It goes further than this. Canon is both an electronics company, capable of producing its own sensors, and an optics company, while Sony is primarily an electronics company, which has only recently started to make forays into optics, since acquiring Minolta. There is no reason Canon can't make a play for the lucrative phone market, so far dominated by Sony, by producing combined sensor-optics packages containing either a standard-sized sensor with a more capable lens, or a bigger and better sensor with a lens covering the same angle of view, in the same size and price range as current phone camera packages. Or the drone camera market, with a large (1.5x/1.6x crop or even full-frame) sensor and lens in the same durable, lightweight package and price range as current small-sensor offerings. You couldn't do either with classical optics - you'd run into size and/or cost limits. But new developments in optics allow capabilities which would previously have required many large, heavy glass elements to be constructed using far fewer, lighter elements, in a smaller overall package. And this is where Canon has a huge lead over Sony, and could potentially capitalise on it, particularly outside of the 'performance-over-all-else' subset of cameras.
To compete with this, Sony would do well to pick up some more optics capability. Sigma, perhaps, or even Nikon. Maybe, somewhere in Sony's boardrooms, some committee has a hidden goal of trying to cripple Nikon financially, while retaining their technical expertise, making them ripe for a takeover (Sony could buy out Nikon now, but it would cost them a lot). Canon would be able to buy them out too, but would have far less reason to; essentially, their only reason to do so would be to keep them out of Sony's hands, and, given the relative sizes of Canon and Sony, a bidding war could cripple both of them.
