Evolution question

Caught in the wild, or evolved yourself makes no difference.

Evolved pokemon are not inherently stronger than wild caught pokemon. I'm not even sure exactly what you mean by this because all pokemon are obtained in the wild or from eggs and are then evolved.

What determines the strength of a particular pokemon among others within its species is its IVs (individual values). Attack, Defense and HP can all be anywhere between 0 and 15 for a wild pokemon. They will be between 10 and 15 for the ones you hatch. There's a higher chance of hatching a strong pokemon than that of catching a strong pokemon. But once you have it, you have it, it doesn't matter whether you hatched it or caught it. IVs don't change with evolutions.

That's true only for GBA or DS, 3DS Pokémon games. There, a trained Pokémon gain EV (effort values) points. That's why they are better than wild Pokémon.

If you catch an evolved form in the wild, it is what it is. If you evolve it yourself, you can select which one you evolve. Since unevolved forms are easier to find and catch, you are more likely to evolve a strong Mon than find a strong evolved form in the wild.