I know their automotive line of filters are currently Champion E-Cores, which Fram recently took over. As far as the lawn mowers and heavy/ag equipment I don't know.
I have a couple of Deere diesels and the filters are just like the rest of the engine, heavy duty, rated for 500 hrs. service intervals. Whoever is making them are following Deere specs,so specific manufacturer shouldn't be an issue.
One thing I have noticed, for whatever reason the lawn/garden filters seem to be over-priced, whereas their automotive/ag/heavy equipment filters are in line, or many times cheaper than the competition.
Deere is also a FleetGuard filter distributer, so if one doesn't like the Deere offering FleetGuard is an option.