I would say not a ton of difference, but you do get some good info if you know it is php vs apsx. The dotNET framework has built in XSS protection and the flaws in each version can be found online. This will greatly help you in your attack.
Knowing which it is running can help speed up the test since you can make some assumptions about the underlying OS and RDMS. Don't forget these are assumptions and should be treated as such. A big problem I have seen is people following assumptions as if they are truth.
If it is running dotNET code you know it is windows and there is a much higher probability of the underlying database being MSSQL. If the server is running php the server is most likely a flavor of linux and more likely to have an open source RDMS backend such as MySql or Postgres. These are useful for exploiting a SQL injection vulnerability or accessing local resources if you find a local file include vulnerability.