An Earth-sized moon will have almost a hundred times the mass of Luna, which will mean much bigger tides. Re-arranging the Earth's geography like that will probably dramatically change the climate, for instance I think it would probably stop the gulf stream and make Europe's climate colder (and I think you might get a lot of violent storms and winds in all those latitudes where there are now more-or-less planet-encircling stretches of open ocean). Civilization will probably recover sooner or later, but this climate change will be very disruptive, and when civilization recovers it will look different (e.g. with a dramatically cooler Europe the regions near the Mediterranean shore will firmly stay Europe's cultural, economic, and demographic center of gravity, while Britain and Germany will stay backwaters now that they have a climate similar to Canada, and agricultural civilization in Scandinavia may collapse altogether, leaving that land to be inherited by the Sami aside from some fishing villages on the coast). Tides a hundred times stronger probably means huge stretches of coastal territory becomes basically uninhabitable giant beaches and swamps, and will make ocean voyaging and ocean fishing much more challenging.
If Europe becomes dramatically colder, I think the Middle East might benefit. Looking at a world map and assuming a general rule of "the new climate resembles North America at that latitude," the Middle East, North Africa, and southern Europe will now be right in the temperate band between 30-45 N, while Germany and Britain will now have a climate similar to southern Canada. I think the Middle East and North Africa may become cooler and wetter? If so, maybe in the long-term Islam takes over the western half of world? A colder Europe suggests a probable re-emergence of something like the Mediterranean-centered civilization of the late Bronze Age and Greco-Roman period, but on the other hand the huge tides will make civilization more firmly land-based so the Mediterranean may become more firmly a natural barrier that divides instead of an easy trade/transportation route that unites.
If we ignore the effects on tides and climate (assume the ASB magically keeps tides and climate the same)… I suspect the Aztec empire won't last very long, because the whole mass human sacrifice imperialism is going to create a lot of resentment. The Inca were less evil and their empire may endure. In the long term the fate of Americas + SubSaharan Africa + Australia world is going to depend on whether somebody establishes regular contact between the Americas and Africa, and if so what that looks like. The Africans have iron-working, so they could give a big tech boost to the Americas (on a less cheery note, they also have Eurasian zoonotic diseases, but this world's equivalent of the Columbian Exchange may be less bad than ours).
First contact happens when one of the worlds builds a moon rocket, or when both worlds build radios. My bet is on Eurasia-world building a moon rocket first, and probably landing on Americas + Africa + Australia world while the later is still preindustrial. I suspect with no New World crops and resources Eurasia-world will have slower technological advance than ours though, so first contact might happen when Eurasia-world sends its first manned expedition to the moon in the year 2438 or something like that. Though I think Americas + Africa + Australia world might actually have more fertile land, so if regular contact and technological and cultural exchange is established between Africa and the Americas at some point I could see it happening the other way around, with Americas + Africa + Australia world sending moon rockets to Eurasia-world while Eurasia-world is still preindustrial.
