Actually I can argue that technically Asp.net is faster than PHP I know that since my "schooldays". But yes I didn't see forums faster than PHP. I recommend Vbulletin and PHPbb .)
If you want to integrate with an ASP.NET website, then you really need an ASP.NET based forum. Both vBulletin and PhpBB are Php/MySQL based.
If your building relatively small applications / websites then php/mySQL is fine, but for larger stuff where you have a team of designers working on it then ASP.NET is the way to go. PHP was not designed for large team work projects and is not really suited to them, which is why most very large complex sites are not built in php.