The ones I keep in the garage, I cover with the standard cover. When I take them outside, I put the deluxe covers on. I have a bunch, so it works good when you are rotating grills. It its inside, it'll get a standard cover.
I just got ready for hurricane season. last year my garage was under water from Superstorm Sandy. All my grills are now raised off the floor. Hopefully I won't have to do that again!