If you simply change the version of ASP.NET using the ASP.NET tab of the new site, the changes will apply only to that site.
What you need to ensure that you are not trying to run ASP.NET 2.0 and ASP.NET 4.0 applications in the same application pool. If you do this, you will encounter this error:

You will also see this audit event in the application event log:
Event Type: Error
Event Source: ASP.NET 2.0.50727.0
Event Category: None
Event ID: 1062
Date: 01/12/2011
Time: 12:31:43
User: N / A
Computer: KK-DEBUG
Description:
It is not possible to run two different versions of ASP.NET in the same
IIS process. Please use the IIS Administration Tool to reconfigure your
server to run the application in a separate process.
Create a new application pool for your new ASP.NET 4.0 application (you can do this by cloning an existing pool):

Then assign a new ASP.NET web application for this pool on its property pages:

Kev
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