So, in order to get an idea of how to answer the OP's thread title question, I did the deed. I made a fresh character on Bahamut to experience how others play. I took notes on some things of interest. Here they are in no particular order.
1. There is only one JP seller yelling and they yell at exact 10 minute intervals so that is a change of pace from Asura where there are at least 5 people yelling to sell JP at any given time and they are riding the cool down timer of yell hard.
2. There is quite a bit of people with hodge-podge gear walking about. Sets that seem to be mid-completion towards something. I'm used to seeing people walking around in town in full idle sets with maximized refresh/regen/-DT/movement. Not to say the players I see are bad in any way. It just kind of surprised me how people don't walk about in idle sets as much.
3. It's weird not having 25 people AFK around nearly every in-city homepoint.
4. It was quite refreshing not having crafting shield bots hogging all the quest item dropping monsters. I was able to get my entire Bastok 1-3 Quadav Fetich piece set with no competition. No bot running back and forth at LV51~55 level cap items either.
5. Yell is nearly dead silent. I had expected less yelling, but did not expect no yelling. I yelled when Fire weather popped in the d00ns and it stayed in the list of most recent yells on this site for several hours. Someone sent me a tell thanking me, so at least I helped one person by breaking the silence.
6. The people are basically the same. I picked up a linkshell and found people that were nice. They talk about the same things we talk about in my linkshell on Asura. I never bought into the "Asura players are the worst" thing because I knew better and it was nice to have it proven to me via first-hand experience.
7. It's weird having things on AH sit on AH for more than a single day. Initially, on a brand new character on Asura, I would begin accumulating money by farming certain things. To start, it's Mandragora Dewdrops and Bee Pollen for the RoV quests and/or Gausbit Grass for the chocobo license quest, and then I move to farming things that sell even higher as my level increases. With the population of Asura always bringing in new characters, Dewdrops and Pollen are always quick sellers for decent gil to get me into my initial magic scrolls and such. It was weird having them both sell for less and take longer to sell.
These are just a few notable things that respond towards the OP's question. Hope this insight helps a bit. I'll make note here of anything else I notice.
Edit: Oh, and while it's not every time I zone, I do often end up being able to see Apururu's Unity chat a lot more often. That's nice if I was trying to do some Domain Invasion. Currently leveling WAR, MNK, THF, RDM, BLM, and WHM to 50 while I try to decide a main though so Domain Invasion is still far off.