What you are describing falls into a 'management decision' vs. a technical one. Technically if your site static content, then HTML is the best way to go. There is a slight risk of being vulernable using ASP. There has been one ASP exploit in recent years. MS has a patch for it.
Regardless, I think the topic should be not if you use HTML vs. ASP rather a security and locking down your server discussion. If you don't need or use ASP, then turn off the functionality. If your site is a brochure site, you can remove all the dynamic script mappings that support ASP, ASP.NET and others.
In the end, regardless how you go, I think the risk is about the same, it's splitting hairs. If you are looking for a better, more secure way, HTML will win. "A server is only as good as the person(s) administering it.". Hope there is some advice in there. :)
Steve Schofield
Windows Server MVP - IIS
http://weblogs.asp.net/steveschofield
http://www.IISLogs.comLog archival solution
Install, Configure, Forget