I've been happy with the Timbuk2 bags. I have the medium size "Snoop Camera Bag" which easily holds 60D w/BG and mounted 24-105L, 100-400L, 100L macro, 50 & 85 primes, small flash plus usual other stuff (cards, filters, charger sometimes). I also have a regular Timbuk2 messenger bag in small size to which I added the "Snoop Insert." Small bag holds 60D w/BG and mounted 15-85 zoom, 430 EXII flash, 70-300 zoom(non-L version), plus cards, etc.
Obviously the medium is the outdoor, nature bag. The small is more indoor oriented; but things get rearranged often as needed. The small is clearly easier to carry all day. I can't say if the 5DIII w/grip is enough taller than gripped 60D to be an issue. Messenger bag with carry handle plus the shoulder strap is best.
There is an extra small Timbuk2 version available; but I already had a Mountainsmith Aurora II AT to hold the OMD-EM5.