Scripting languages are often like religion, and people pick their favorite for reasons that sound rational to them, but not to those who subscribe to a competing one.
I use ASP mainly because that's what the servers for my major client use. I use PHP for websites that are hosted on servers that have that available rather than ASP. There are things I like better about ASP than PHP, and things that I prefer in PHP over ASP.
If you're most comfortable with objects, then JScript ASP does those MUCH easier than PHP or VBScript ASP. Later versions of PHP have objects added into them, though, that remind me a lot of C++ classes. Overall, though, it's more procedural than object oriented.
Overall, I'd say it's not a matter of which is "better", but which one the web server you're using has, and if both are available, which one provides the functionality and comfort that you want. With both as popular as they are, it'd be wisest to learn each and make yourself that much more flexible and capable.
Lee