I think that PHP is the best. I don't know why to change something that is working fine. You are saying that PHP is not running on Windows servers? I don't think so. As far as I know PHP is running on every server. So I'm for PHP.
PHP is a C++ based language which is very rich and capable but it's stored as script. ASP is stored as script, but most ASP work these days refers to ASP.net, which is compiled. ASP.net needs to be developed in Microsoft Visual Studio - which you can get for "free" under the Dream Spark Programme - which I highly recommend. VS is a rich environment, works with Enterprise level databases (There is no comparison between MSSQL and MySQL in my opinion)
Both programming languages are used in very large web applications and large successful web sites so there should not be any doubt to the ability of any of the above programming languages to handle a large web application project.