For thick bars, it is typically diameter that is referred to. I have 3 sizes of thick handled dumbbells - 2", 2.5" and 3", and I can easily say that once you get above 2" it gets REALLY hard to manage most lifts with that kind of size. For example, I've done dumbbell rows with an e-z curl bar as a DB and managed 5 reps @ 150 and 3 reps at 165, but with a 2.5" bar my grip is dead for a continuous hold after the 4th rep at 115. Everything suddenly becomes a lot harder to do as you have to worry about grip giving out before the other muscles do. Definitely fun stuff, and it carries over well to a lot of other things. Pinch gripping gets easier, and when you go back to grab a regular bar it'll seem like a toy. If you can get your hands on some thick bars, definitely do it and you won't be disappointed.
If the Ironmind ones are too expensive, I highly recommend the Fat Bastard Barbell Co. ones that I have - a fraction of the cost, and the shipping will be much better than whatever IM decides to hit you for (their outrageous shipping charges are my only complaint with them!) Check out www.fatbastardbarbellco.com
for more details!