I most commonly see DOORS Web Access (DWA) installed on its own server and I prefer this for two reasons:
DWA is resource heavy. It wants RAM and CPU. The DOORS Database server is not resource hungry and can run on an old server with as little as 2GB of RAM. If you add DWA to such a server, the server will have to be upgraded.
Upgrading DWA impacts all DOORS users and the risk is greater than if DWA was on a dedicated server. Upgrading DWA is almost certainly going to require the database server to be restarted. There can also be the occasional DLL compatibility issues if DWA is upgraded but the server is not.
An important related note is that DWA should be close to the DOORS database server. A ping should be less than 50ms between where the database server is running and where DWA is running. I have twice seen DWA put in a remote location (a different city), with ping times significantly in excess of 50ms. The performance was unacceptable with operations such as login and opening modules timing out.
In summary, keep them close but not together.