I love the MONO cases, and they're my go-to for any gig where I am hand-carrying my guitar.
On tour (by ground or air), I use SKB iSeries cases. They're ATA-approved flight cases, but are significantly lighter than an Anvil-style case; I'd say they're probably about 30% heavier than a standard injection-molded guitar case. They're waterproof, have multiple handles, and a handy set of wheels on one end for towing like a suitcase. As near as I can tell, they are indestructible. I never feel 100% comfortable handing off my guitar when we fly to gigs, but so far this case has done a perfect job of protecting my instrument against the nightmares of baggage handling.
Most airlines will allow you to bring an electric guitar onboard in a gig bag if there is room in the overhead bins for it, and therein lies the rub. Because most airlines charge per bag, travelers want to bring their carry-on bags aboard. That means the bins are usually quite full, and even if you do happen to find one with room for your guitar, someone will not realize there is an instrument in there, and will attempt to cram a suitcase in on top of it. Not cool. If there isn't room for your guitar in the bins, the airline will require you to check it with the baggage, which is a terrifying prospect in any gig bag. I just pack up my guitar in that iSeries case, check it as baggage, and say a prayer to the patron saint of wandering minstrels.