In fictional world, a nuclear apocalypse has destroyed old nations and ravaged civilization. Refugees (and colonial settlers from before) from the mainland fled to unaffected Africa and North America/Greenland. The two Americas are not connected via land (South America merged with Antarctica in the ice age) in this alternate world. A large Alps-sized mountain stands between Africa and Europe. No airplanes have been made for centuries as the skies have been very hazardous after the nuclear war.
2-2.5 centuries have passed and the radioactivity has vanished completely. The two sides have gradually built two empires of different culture and almost same technological level. After explorers declare Europe and Asia suitable for living, both sides, aware of each other's existence but unaware of their military capability, race towards the mainland with their navies. N. America has a navy the size of current US navy, 90s tech. African navy is twice as big in tonnage but 60s tech. In an all out naval war, who would win and how exactly?
I'm gonna make things a little more clear..
1.The African empire is not exactly African as it is ruled by a nobility of European ancestry from the pre-nuclear war colonial times.European leaders and soldiers make up the majority of the military and political leadership.
2.North American empire is similar to the USA but with a fascist-theocratic government.The African empire is an absolute monarchy with mostly European aristocracy.