After uploading and reuploading all upgrade files (1.1.3 to 1.1.4) I get this " Error
An upgrade was found for a version of XenForo that is newer than the uploaded files. Please reupload all of the files for the new version and reload this page."
Presumably this relates to the "stat" setting for PHP. It decides if APC should check each file that has been cached against the local one on disk to see if it has been recently modified? With stat=1 enabled, if the file has been modified it will recompile the PHP code and cache the new version. With stat=0 it will not check and use the one in cache.
The benefit of having it on (1) is that any time you make changes to a PHP file you will not have to manually flush the APC cache to see the changes live. The downside is that it creates a slight performance hit as each file must have an additional stat() call to check for the file modified time.
It's usually advised to turn it off (0) in a production environment - presumably on the basis that you're not going to change things very often, so will benefit from the reduction of stat file modified checks - but for pushing out an XF / add-on upgrade you'll probably want it set to on (1) for ease of use.
NB: I use Apache so flushing the cache manually is just a case of restarting Apache.