AzerothCore is a core based upon SunwellCore which is based upon TrinityCore.
I'll quickly talk about why custom server developers should use it, especially people with new gameplay ideas as it's often the case on modcraft.
Sorry if it's not well structured or if it's lacking information.



Advantages over TrinityCore


Better for players
It has been mainly worked on by private server developers unlike TrinityCore (many devs there aren't interested by making playable private servers at all). Almost everybody who contributed to AzerothCore runs his own small public server at the moment, so they want as few bugs as possible for their players.
The two developers behind SunwellCore had a server with 3000 players online in January 2016 when they released their code and shut down their server.
The two founders of AzerothCore also worked on their own small private (but public) server.

It translates into a more polished experience for players, less bugs (look at the SunwellCore features), less complaints and a top notch stability. The database is included in the repo (with working dungeons and raids for example).


Custom modules
The core makes use of custom modules which allows us to plug them in and out easily, and which doesn't require us to modify the core files. It also means we can keep pulling the git changes from the main repository if we only work with modules.




Extras features
A better configuration file system which allows us to use a tiny configuration file for better readability and maintenance.
A (very) new feature allowing people to disable some unneeded features to increase the performances.
A script to easily merge all new SQL updates into one without worrying much.
Several custom modules available (such as a Transmogrification module).
Based on TrinityCore, so many things are compatible with AzerothCore or require minimum modifications.
Sunwell team provided custom addons (raid browser and arena spectator) to use as well which should work very well on AzerothCore.
For now, there is no need to extract the client data, it's available as a direct download.


Comparison
Just found this on google right now : old comparison between trinitycore and azerothcore.



Philosophy
The goal is to have a playable server, and to favour custom creation.
This is an explanation of the long term goals of AzerothCore from the founder : https://community.trinitycore.org/topic/12792-can-someone-explain-sunwellcore/




Links

https://discord.gg/PaqQRkd - The main place to talk, come !
http://azerothcore.org/
https://github.com/azerothcore/azerothcore-wotlk

› See More: AzerothCore - The 3.3.5a core made for custom servers