Fur is MUCH warmer. A fur coat with a thin layer of nonwoven insulation between the fur and the lining outperforms most "performance-oriented" warm jackets. I'd say as warm as an expensive, high-quality goose down coat during the first month of wearing, but totally more windproof, moreover many good modern "down" jackets are made of synthetics in reality and don't last long (my last Land's End goose down coat collapsed after washing and the "down" turned into something that looked like lumps of wet kleenex). The closest I've seen, warmth-wise, is good workwear for drilling/oil company engineers (not regular workers, but for those who have to stand in the cold and watch others work).

I have an otter/wolverine fur coat that's so warm that I don't even need to wear gloves most of the time if it's above -20F. I can't say it's much heavier than a good warm synthetic winter coat, because of how well they thin the leather in commercial tanneries.

Many furs are inexpensive and definitely last much longer than synthetics. Sheepskin and nutria coats are popular here this season (which is good, because just like fake fur coats, they are a "gateway drug" to wild furs). Lots of nice sheared beaver coats, too, e.g. here (no idea if the link works from the outside): https://www.spbmeh.ru/catalog/bobyer/

and yes, fur hats are TOO warm most of the time.

I just thought some of you could be curious about what it's like where furs are more widely accepted than in the US/Canada