For a new account, you would get "LPCP" (LunarPages Control Panel), an in-house locally developed control panel. For an extra $2 a month, you get cPanel, which all the old accounts have.
I know the LP staff is going to dispute this, but LPCP is not a finished product. From what I hear, they're still adding base functionality that cPanel has long had. I think LPCP "escaped" too early, under management cost-cutting pressure, before it was anywhere near done. Using cPanel myself, I don't know if LPCP is missing anything critical -- hopefully not, just things that you need to manually edit your .htaccess file for. This isn't to say that cPanel is the cat's meow -- it's very clunky in a few places, such as being unable to add subdomains to add-on domains, and a very primitive redirection facility. Maybe you can look at LPCP as "adequate now and can only get better"?