Case is always better OFF.
Even if your case is off, I recommend having one or two good system fans in your pc.
Sure, dust is going to build up. But it will be almost exactly the same amount as a closed case w/o dust guards. Dust is only a problem if you never clean your case. I clean my case every 1-2 months.
The biggest thing to remember is that with your case closed, your pushing and sucking air from a closed source (Heat buildup). If you have your case open you will be getting fresh cool air easily.
With your case off & 1-2 system fans, the biggest difference you will notice is that you do NOT get any hot spots in your pc. And unless your case is very sturdy, you will notice only a very small increase in noise from having your case open.
Summary......If you have your pc on the floor, keep your case ON. If your pc is elevated then leave it OFF.