Sometimes you adjust AP´s transmit power to max and it doesn´t change anything…
Remember that the wireless communication is bi-directional, and when you maximize power transmit on AP´s your wifi device (mobile, laptop, tablet) is listening harder, lets call "on download", for didactical purposes, but maybe you have a bottleneck on "upload" because the device doesnt have the enough power to the AP listen "clearly", this is common because AP´s antennas are better than antennas encapsulated on cellphones, for example...
In less words, with more power your device will listen your AP far, but it doesnt mean that your AP will listen your device.
I prefer to upgrade AP´s antenna if its possible, the gain is both transmission and reception, instead of maximize power that the gain its just in transmission.