They're equivalent. Neither is more correct. Megawatts are a bit more understandable to the layperson, for the same reason that "a million dollars" is more understandable than "a billion dollars". A megawatt is about 1000 homes[1]. A gigawatt is a city.
I guess it's similar to how we in the metric world would say "2000 kilometres" and not "2 megametres" (certainly not in an everyday context).
> "a billion dollars"
This is only tangentially related to your point, but the word "billion" often gets mistranslated due to its two distinct meanings (long vs short scale). This could be another reason to avoid it.
The best distinction I’ve read between a million and a billion came from Bill Bryson. He noted that there are 1 million seconds in 11 days. There are 1 billion seconds in 32 years.
[1]https://www.eia.gov/tools/faqs/faq.php?id=97&t=3 A US Household uses slightly more than a kilowatt on average, though obviously peaks and troughs are well off that.