I think some people just really suit country living and others city, and you should go where best suits your ideals and lifestyle. But other than fresh air, I don't think rural living is better for children than city.
I live in a city in a high crime area. What I love for my children and couldn't give up for just fresh air:
Having many ever changing free museums and galleries less than 5 miles away.
Lots of parks and playgrounds to explore
Never having to wait more than 15 minutes for a bus or train
Being able to walk to libraries, cafes, super markets, school, bakeries, restaurants, takeaways, doctors, swimming pool, cinema etc. I'd had to have to drive everywhere.
Not being a slave to the weather.
Not having to plan full days out, we can go out for the morning or afternoon on a whim as we can get to so many places more quickly than if we were living rurally.
Having Amazon Prime, Prime Now, Click and Collect, same day Argos deliveries, Just Eat, 24 hour supermarkets and garages and Uber Eats. I don't regularly use all of these but knowing the option is there I like.
Living in a multicultural area, having international food markets on the end of my road. My 3 year old didn't know what a date was in a book last week so we walked to the Turkish Grocers and bought some Medjool dates for lunch.
I can always find free events in school holidays, be that a Bear Hunt in a park or arts and crafts in a shopping centre.
My kids to to forest school, and we go to beaches a lot and spend so much time in parks and woodland I don't feel like they are starved of nature.
I did live rurally for a while and hated the silence, the isolation, the amount of driving it took to go anywhere, the lack of choice of local activities, that never ending Sunday afternoon feeling, the lack of indoor activities and the miserable weather. I always felt much more nervous going for walks in the evening than in my dangerous city at night, and forget it in winter when it's pitch black.
But if you love rural living, do that. The kids will be happy whenever you are.