Which ASP or ASP.Net
ASP is older, and only supported by Windows.
ASP.Net is newer, and actually superseded ASP - ASP.Net is able to be emulated mostly on x10hosting's servers via the mod_mono project, which Illuminated and Premium hosting do have. The x10hosting comparison page also explicitly states ASP.Net using mod_mono - There is a large difference between them, as one is 100% Windows only, while the other can be partially emulated on Illuminated and Premium servers
Because of ASP.Net being emulated via the mod_mono project, not 100% of all ASP.Net code will work as expected, and in addition some code will actually not function at all. ASP.Net is supported, but if you must have ASP.Net working as intended, you need to find a Windows host, as that's the only guaranteed way that ASP.Net will perform as expected you should look at [
http://www.mono-project.com/Compatibility ] - it shows what sections do not work - and some of those sections might be critical to the project you are running