I own 1 mare, 2 geldings, and soon buying another mare, and I've noticed that I pick horses with a strong/goofy personality, so even though my mares aren't moody almost at all and my geldings are just like big kids... I do prefer my mares. BUT I've have a lot of exposure to many geldings, stallions, and mares over the years from working at a big riding stable and to be honest, it really does depend on the horse.
I've handled, ridden, and been around evil/smart/sweet mares, stubborn/stupid/kind geldings, and gentle/dangerous stallions. My mare, Athena, never gets moody while she's in heat. I never really keep track of her cycle, and since she never gets moody around that time the only way I know is when she flirts with a gelding from across the fence. One of my geldings, Snafu, at 7 years old is just a big kid, literally. He chews on everything. Not like wood, fencing, things like that. I mean reins, cross ties, brushes, he'll carry food buckets around for fun, and he's extremely playful. But his favorite thing to do (and Playboy's too) is to play the 'Halter Game'. Where two geldings play fight while trying to get each others halter off. It's really fun to watch them play, but I've never seen a mare do this. Snafu tries this with Athena all the time, and every time she just gives Snafu a dirty look like 'Let go of my halter, you idiot!' and then wanders over to the round bale.