Surely it depends on what sort of overshoes.
I only tried neoprene overbootees for one winter - hard to get one and off (over mtb shoes not road shoes, it has to be admitted), zip failing after a couple of months but nursed on to finish the season by which time the whole things were falling apart especially the soles, sweaty feet which quickly went cold if I stopped (so OK for a commute but not for longer rides). In general, windstopper + lycra overshoes have been more robust, lasting 5+ years, and are fine for cold dry or snowy conditions (and very cold with electric foot heaters) but not so good in rain.
So the upshot has been winter shoes - first Sidi then Shimano and now Specialized - which I wear for day to day cycling as they cope with walking around shops etc. better as well as easier to put on and off. But I usually opt for the windstopper overshoes + foot heaters for longer rides in cold weather (I tend not to do long rides when it's raining
- old age is turning me into a fair weather cyclist).