Pro Clear, straight-forward user interface
Well I suggest you check it out for yourself, but what I like most is that it's simple yet effective: no bells and whistles, simple black/grey/light-blue/white color scheme, it's immediately clear where you have to go for each specific task, and build settings pages are like that as well. Getting a 'standard' build running literally took me a minute the first time I used it.
Con Configuration is limited
AppVeyor's configuration (which is done from the .yaml file in the root of the project) is unfortunately very limited. The configuration is either tied to a branch or, in other cases, it's global. This limits the developer to a single build process.
However, since you can use arbitrary scripts for building, all those limitations can be overcome. Configuration can also be done from the web UI without a .yaml file.