What’s your definition of “better fate”? You’ll be in a foreign country with no network/resources and when the global supply chain shuts down most people everywhere will starve.
No nuclear fallout to speak of (you can go outside and it's safe, unlike in Northen Hemisphere). Much milder temperature drop.
Covid era taught me how to stay put really long, so I'm gonna be prepared. Southern Hemisphere has plenty of cultivated land, so I only need to hold out until trade routes are somewhat restored. (From that point of view it's better to be in South America, but given their crime rate I'd rather be somewhere else during that time)
I won't quibble with your if the world goes nuclear scenario here but I would ask; how lnog can Mauritius self sustain without outside trade for fuel and food reserves?
It's an island that grows some food, of course, but how much relative to the population?
It definitely is not self-sufficient when it comes to food. But trade routes are pretty low tech things, we've been having them for thousands of years, I expect them to reappear quite fast.