There are three types of servers. The biggest one, Asura, where everything is always for sale, decent prices, there are tons of groups doing things and even merc groups for you to buy from, but if you want to do anything on your own, you will have massive competition for any NMs worth doing (REMA stuff, basically).
Hybrid servers with mid populations still have a little competition and decent availability for items on the AH, but I think this is just kind of the worst of both worlds.
Low pop servers have virtually no competition for NMs at all, so if you want to farm something, it's always safe and available for you to get with no issues. The only problem is if you want to do group content, you need to find one of the few active linkshells running, and like the people in them. There's not a lot of options, but we are tightnit groups and you can usually get into one of them since we don't have any merc groups. The availability of crafted items is also fairly low, so you either need to pay out the *** for them or ask one of the crafters to make them for you, but this is cheaper and they will likely do it for very little cost or free if you are friends with them.
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Personally, I do not ever want to fight for NM claims again. I played in 2003-2010 or so and it was absolute hell to claim anything. Endgame and being in HNM Linkshells was the absolute *** worst. So I prefer low pop servers like Carbuncle and will never go to a higher pop server.
Even people who do HEAVY crafting and can't find a good market on Carbuncle still stay here as their main server for that reason, they just pay for server transfers to send mules to other servers to sell/buy stuff and come back. That being said, if you do want to craft a lot and don't want to pay real money to transfer, low pop servers might not be a good fit. As someone who doesn't really craft though, I couldn't care less.