SPEAKING GENERALLY about male dogs...

Male dogs tend to be more stable in mood than female dogs -- less prone to emotional swings.
Some male dogs are bolder and more aggressive than females, while other males are "goofy" and "klutzy" -- "big softies" and "good ol' boys".
Male dogs have genitals that are easy to see. When you roll them over to rub their belly, there's -- how shall I say this? -- "something in the way". Some owners feel self-conscious about that. Male dogs may also become aroused and/or lick their private parts, and again, some owners find this embarrassing, especially if Grandma happens to be visiting.


SPEAKING GENERALLY about female dogs...

Females are more prone to mood swings and emotional theatrics. Females can be very sweet and loving when they're happy -- but grumpy if something isn't to their liking.
Female dogs are experts at The Dirty Look and The Sulk.
Female dogs are less likely than males to be openly defiant or to engage in blunt power struggles with you -- but they are opinionated and often manipulative.
Female dogs squat to urinate, so they pee more neatly and unobtrusively than male dogs. Some dominant females, however, DO make a credible attempt to lift their leg -- these female dogs will often mark territory much like a male. If you own multiple dogs, a dominant female may scout around sniffing for places where the other dogs have peed, so she can "cover" it with her own scent.