By "stand alone web server" do you mean embedded in your application? I've never used Indy, but I have worked on several Java apps using the Jetty library. The main advantages of this over an Apache/IIS proxy to an app server are easier deployment and configuration since the web service is tightly integrated into the app with nothing extra to install.
If you have existing apps though, and this new app is permitted to be deployed to the same environment, I'm pretty sure your sys admins will want you to use the existing app server. Nobody likes extra operational complexity even if it's slightly easier for you to build. Adding another app to an app server is trivial.
Other considerations are:
Security: Network config, log files, access controls, etc. will all have different implementations from your Apache/IIS systems and different usually means worse security. Simple things like SSL authentication that your sys admins understand with Apache/IIS will work differently with an embedded web server.
Performance: The embedded server is probably a little more efficient, but a little less scalable. Your coding decisions greatly impact this and with embedded servers it's easy to screw it up.
Development: I find embedded servers much easier to work on since I can run them as simple Java apps instead of web apps, e.g. an Eclipse Java view instead of J2EE view with Tomcat integration.
I know this is answer is from a Java viewpoint, but I hope the general ideas apply to Delphi.