Developer who knows both C#(Asp.net) and PHP, what would you prefer to select for Today's world Website Design(Either Static or Dynamic sites)and Why?

Depends on the requirement of the application design.

Website was normally static; but now comes with lot of dynamic "content". The term "content" is very important.

For Applications, it completely depends on the requirements. ASP.NET is good for dynamic content; not much worked in PHP.

Check the requirements first. Then decide after analysing logically every point. I prefer, paper work drawing, though considered old fashioned.

Website design doesn't depend on PHP or ASP.NET.  If you are talking about the Interface of web application. You could choose any one from php or asp.net to implement any website design.