I definitely play way more differently when I'm playing as Babylon. I've come to realize that there were so many techs that I don't bother to get the eureka and brute forced, which I can't ignore as Babylon. Trying to hard research any tech as Babylon is quite infuriating! Highly recommend not doing that! I do really enjoy not being chained to building Campuses everywhere though.
Let's see...
I normally ignore Aqueducts, but being able to find Niter early is too important to pass up on. Need to make sure the Aqueducts are in a good place for Industrial Zones as well.
I never ever ever build Forts, but Field Cannons and Cuirassiers come from Ballistics, which wants 2 Forts. Forts come from Siege Tactics, which wants 2 Bombards, which I'm likely to build anyway but getting Niter very early on can be difficult...
I usually don't build T3 IZ buildings, but now I need not only 2 Coal Plants for Refining to reveal Oil, but also 2 Oil Plants for Advanced Ballistics.
I still find that I want at least 2 Campuses, not just for the Recorded History inspiration, but to also help with getting a Great Scientist to unlock Education.
I should definitely be building Theatre Squares earlier, not just for the culture, but to also get a Archaeological Museum to unearth an artifact for Combustion.
I still haven't figured out how I'm going to get a National Park before or upon reaching Radio...
I think I might have to settle for hard researching Chemistry, since it requires completing a Research Agreement...
This list is not exhaustive of the new things I've had to keep track of. There's quite a lot!