There’s an FAQ on bulb/dimmer combinations that have issues and why that can happen. Basically it’s a combination of the fixture, the bulb, and the switch, so sometimes it’s just trial and error.
The GE switches have a narrower dimming range than most of the other brands, they won’t dim below 10% while both the Cooper and the Leviton do and sometimes that’s the source of the problem, that is the flickers happen in a range that the GE doesn’t even try to access. But multiple community members have reported issues with the GE switches as well in some circumstances, again sometimes you just have to try it yourself and see.
As it happens, the video in the FAQ thread is using a GE switch and you can see buzz and flickers on a couple of different bulb brands.
Back to the original question…
Eaton is the company, Cooper is the division, Aspire is the design style, and Aspire RF is the Z wave model line. You can find the devices sold under any of those names.
Both Leviton and Cooper are good devices. 
Both have licensed the instant status patent and offer a number of configuration parameters. Leviton has updated their line with zwave plus versions, which is always good, but they do cost more and personally I like the color and style combinations for the Cooper better, but that’s just personal aesthetics.
The Cooper line includes a battery-powered switch looks identical to the mains powered one, so some people choose them just so they will be able to mix and match those. Cooper even has a special underplate so you can put a battery powered one right next to a mains powered one creating a double gang where there used to be a single gang and it will look really nice.
Cooper has a couple of special features like child lock and panic mode, but setting those up to work on the SmartThings platform can be complicated and these days you can generally do the same thing in other ways.
Leviton uses physical traveler wires for its auxiliary switches in a three-way set up, while Cooper uses RF, so that can make switch placement a little easier. Again, it just depends on your own needs. And of course with SmartThings you could use two Leviton master switches on different circuits and have them follow each other if you wanted.
Whenever you want to check zwave certification for any device, start with the official Z wave alliance product site and look up the device there. If it certified for Z wave it will be listed if it’s considered a current device. (Some older EOL devices may have been previously listed but not have a current listing.)
https://products.z-wavealliance.org
The AL series from Cooper are definitely Z wave certified, they just choose not to put that in the individual product descriptions in the marketing materials, which is their decision. It is in the top level description of the aspire RF line, as well as on the technical spec sheets.
They used to feature it more prominently, I think they are trying to avoid calling out the fact that these devices are not Z wave plus, as Leviton has now been pushing that in their own marketing materials. 
So different people have different preferences, just depending on the specific features you’re interested in. Choice is good.