I like the "Irish" solid coloured (saffron & green) kilts, in fact I'd like to add a green one to my wardrobe one of these days (this type/colour was adopted by the Clan O'More society as our "official" kilt a few years ago).

I also like the various tweed kilts. Not only do I think they look good (especially when paired w/ a matching tweed jacket & waistcoat), but I'd like to have a couple just for knocking about / outdoor wear (i.e. hiking, etc); to save wear on a clan tartan kilt

I really don't think they need be worn any different than a tartan kilt, other than some colours of tweed might be more appropriate for evening social functions than others.