It is also likely that the node will run all three modes - Adhoc, AP, STA. STA hooks to an Internet router if available. AP is for normal PC/tablets. Adhoc is for mesh traffic. This is a common BATMAN configuration and why most people use the AR9331 for BATMAN meshes. Many wifi chips can't run all three simultaneously and AR9331 is one of the few that can. RT5350 cannot so that's why you don't see it used in mesh nodes.
Running all three modes is a lot for a tiny chip like an ESP8266. So in a mesh I'd expect it to only run Adhoc mode and not function as a main routing node. This is another area where mixing chips makes sense. Build larger nodes using the AR9331 and then make mesh only nodes using the ESP8266. TL-WR703N is a very popular AR9331 router - $20.
BATMAN is used a lot since it will route across mixed networks - ie wired links between nodes are allowed. The links have different weights and BATMAN will preferentially use the wired links. A few strategic wired links makes large, campus wide BATMAN networks possible.
http://www.open-mesh.org/projects/open-mesh/wiki