Do you have other sites or services on the server that use this app pool and could potentially provide a security risk for database access? If yes, create a new app pool. Do you have another site that might cause the app pool process to crash, or might have a memory leak (thus affecting other sites in the same app pool)? If yes, create a new app pool.
Other than slightly more memory usage, app pool isolation really doesn't have any serious downsides. Microsoft "generally" recommends it (although this article is about SharePoint setup, the app pool / database access concept is the same):
You need to establish which Application Pool in IIS is going to be used by the IIS Web Site. Application Pools in IIS access resources on behalf of the Web Site using an account identity that you specify. This Application Pool will be used by the web application to access its content database. Generally, you’ll want to create a new one to keep it separate from the existing Application Pools.
See this thread for some additional discussion of the pros and cons of separate app pools per site.