Show both.
If a user is not "internetally" sophisticated, they don't know what a domain name is. An email has the @ thing. A website has a www thing. There's a conceptual gap we nerds take for granted.
If a user is sophisticated, consider that they still just want to click on something to get to your site. Don't add barriers in the name of aesthetics - they'll get misinterpreted. For instance, I use Google apps to host my email using my name as my domain. There's no web site behind it.
So I might think you don't have a website. If I can assume there is a site I should visit, I'd question why there's no link. Are we paying by the byte here? Suppose I'm on a phone or tablet - copy, paste, edit is still a much more labour-intensive process than on a desktop. Having to go through a bunch of long presses and app swapping because I wasn't given a link has already started to annoy me, and heaven forbid I make a subtle typo.
I see where you're coming from, though. If your domain name is long or looks a little funny when stacked vertically with the domain as part of an email address, consider replacing the URL with an HTML link with simple text like "My web site". This does, unfortunately, not work for users using plain text email clients.
As with Steve Krug's Don't Make Me Think principle, I think we should also consider that to mean Don't Make Me Work.