Generally speaking local food was ‘vine ripened’. That is to say - it didn’t need to be harvested long before it was ripe and then shipped halfway around the world.
The biggest difference this will make is in taste if you’re looking at fresh produce. For instance, in the north eastern US, strawberries in early summer are cheap and delicious because they are grown within driving distance of your grocery store. In the fall or winter strawberries are more expensive and don’t taste quite so good since they’re coming from (usually anyway) somewhere in the southern hemisphere
This is also why we see peaches in abundance in July/August but they typically aren’t even sold the rest of the year because they can’t be picked and shipped.
As for specific health differences between these two approaches - I’m not sure. I stick to local or regional things when possible, and where there’s the biggest bang for your flavor buck. Bananas are available year round for me but are never local, and honestly I can’t tell the difference between in and out of season. Other things it is more important - blueberries for instance I buy in large quantities all summer (they are cheaper and taste better) but I don’t touch them in the fall or winter. Same for tomatoes - I love a fresh local tomato and will eat tomatoes like an apple at this time of year but the ones we get in the winter that are white inside aren’t edible in my opinion.