No, Female Pokémon are NOT stronger than Males!
In some species of Pokémon, the Females have different features and/or a different appearance to the Males, but they do have better stats than the Males. For example a Male and Female Pikachu have different appearances to one another (see below), but they do not have different stats.
(Male: Left | Female: Right.)
In some species of Pokémon the Males and Females have different Abilities to one another, for example Meowstic; a Male Meowstic's Hidden Ability is Prankstar, while a Female Meowstic's Hidden Ability is Competitive. However they have exactly the same stats.
Just because you beat your friends best Pokémon (which so happened to be Male) with your worst Pokémon (which happened to be Female), does not certify that a Female Pokémon is stronger than a Male. A number of factors could be of influence including:
- Your Pokémon's level was higher than your friends.
- You had a type advantage.
- You got a critical hit against your friend.
- Your friends Pokémon might not be EV trained, while yours might be.
- The IV's on your friends Pokémon could be very low.
- It might have a Defense or Special Defense decreasing Nature (you'll deal more damage when attacking than if it didn't have a Defense or Special Defense decreasing Nature, depending on the attack used. Psychical move = Defense, Special move = Special Defense.)