I assume that it should be able to take at least one full Ethernet frame (1500 bytes) but I have not actually experimented to find the limit yet.
I am building a small configuration web server to be used while the module is in soft-AP mode to enter the settings (SSID and passkey) for the actual wireless router that it is supposed to connect to during normal operation. I would like that web page to look half way decent.
I have a quick prototype running (now implemented in Visual Basic because it's much easier and faster to prototype and find my way through it in VB than in C on a microcontroller).