Two different promises
This is the most interesting comparison on the site, because both companies publish a repair route and the routes are not the same thing.
Red Wing resoles. The company runs its own repair shop at the Red Wing, Minnesota factory, and its stores take boots in for resoling with original parts. That addresses the thing that wears out first and leaves the rest of the boot alone.
Danner recrafts. Its published program sends boots to certified repair partners who, at minimum, replace the worn outsole, recondition the leather and restore the original fit and structure. That is a larger job: it treats the whole boot as serviceable rather than just the bottom of it.
Both are paid services, not warranty claims, and neither company publishes a warranty worth planning around - Red Wing's is twelve months against defects.
Construction
Red Wing Heritage boots are Goodyear welted or stitchdown. Danner's Mountain Light is stitchdown, with the upper flared outward and stitched to the midsole. Both are independently repairable by any competent cobbler if you would rather not use the factory route.
The Mountain Light adds a Gore-Tex liner, which is the one component neither program can fully restore. Membranes fail by delamination and clogging, and they are not replaceable in situ. That is the real end-of-life mechanism for a waterproof boot, and it is the argument for buying an unlined boot if you want genuinely indefinite service.
Which boot for which life
Danner if your feet are on uneven, wet, loose ground: trails, forestry, survey work, hunting. The Kletterlift outsole and the mountaineering-derived last are built for it, and the recraft program means the boot can come back from genuinely hard use.
Red Wing if your feet are on floors, pavements and ladders. The flat Vibram 430 and the Amber Harness upper are a city-and-workshop combination, and they are lighter and less hot than a lined mountain boot.
Weight, which decides it more often than people expect
The Mountain Light is a heavy boot. On a trail that weight is support; on a shop floor for ten hours it is fatigue. The Iron Ranger is lighter and still heavy by modern standards. Anyone coming from trainers will find both a shock, and the Danner more so.
The verdict
If you want the boot you are most likely to still own in 2050, it is the Danner - because the recraft program restores more of the boot than a resole does, and because a stitchdown mountain boot was designed for a rebuild cycle from the start.
If you want the boot you will actually wear every day, it is the Red Wing. The best-made boot in the cupboard is worth less than the second-best boot on your feet, and that is not a throwaway line - it is the most common way buy-it-for-life purchases go wrong.