ESP8266 Wifi for http server: What are pros and cons with different libraries/approaches?
Some things you should consider:


How many GPIO do you need? The ESP8266 itself has only two, and RX/TX. Connecting it to an external controller, like Arduino, will give you more freedom. You can only hook up your project to an external SD card for example with more pins. 

If you are going in this direction, you could checkout my ESP8266_PIC library for interfacing the ESP8266 with a PIC microcontroller. It's still very limited and oriented to client development, but it gives you a place to start.
Community support. I have had little experience with the ESP8266 forum but found it little helpful. This might be a reason for deciding against ESP-HTTPD.
Level of abstraction. The Sparkfun example has no abstraction. Everything is mixed up. This won't scale well. I'm not familiar with the others, but they seem more mature projects.
Protocol adherence: the ESP-HTTPD project especially mentions it was not written based on RFCs. I would consider it a bad place to start.
Language: NodeMCU uses Lua script, all others use C(++).
If you need stability, you would be better of with an ethernet chip.