Just picked up a Mono case (I guess I'm a sucker for these high end hybrid bags).
VERY nice (as is the iGig). Very different designs, but both very high quality:
Protection: About equal.... more than a traditional bag, less than the more meaty Sadowsky Portabag (I have one) and especially the very sturdy Slimbag (yep... I have one of those

). The main difference is in the side panel stiffness. The Portabag and Slimbag have hard sides. The iGig and Mono have 'stiff sides', but still with a lot of give.
Weight: Mono is about the lightest hybrid case I've come across. If you are looking for the best 'weight to protection' ratio, the Mono is it
Fit and finish: The Mono has the edge... really high attention to detail and 'design. The iGig has no problems either, but the Mono looks like it should be in the NYC Museum of Modern Art.
Pockets and storage: The iGig RULES. You can fit EVERYTHING in that case.. huge double front pocket and neck pocket. Similar to the very nice Mooradian bags in storage, but MUCH better protection for the instrument. The Mono is at the 'low end' of pocket size (adequate for strap, tuner, cables, and a set of strings, but not much else). The Sadowsky Portabag has lot's of pocket space also, with the Slimcase kind of falling in between.
Strap comfort: Both are great, and both are superior to the Sadowsky Portabag. The current Slimbag model has that very complex 'Alpine Backpack system' that is top of the line if you are walking 5 miles with your bass, but a pain in the **s for the typical schlep from the parking garage to the gig. I greatly prefer the iGig and Mono straps, which are very high quality but 'simple'. Both seem a little more 'meaty' than the very nice Sadowsky bag straps.
Both are very nice. I bought the Mono since its cloth interior seems to be appropriate for the one bass I own that is Nitro finished.
So, if you have some cash to spend, the Mono is king for uber lightweight protection, and the iGig bag is king for massive storage. Both are 'top of the game' for their design goals IMO!