In general:
Not Mega-Evolving: you get to hold an item
Mega-Evolving: (usually) better stats, sometimes also with a better ability
Outside of that, it really depends on the Pokémon. For example, most people prefer regular Garchomp over its mega because Mega Garchomp actually gets its speed cut, doesn't have Rough Skin, and it can't hold a Life Orb or Choice Scarf.
An example where you might not want to evolve your designated mega immediately could be because of the matchup, like bringing out an Ampharos or Sceptile against a fairy type. In their base forms, they don't have a weakness to fairy, so you probably won't Mega-Evolve it until you've KO'd the opponent and it's safe.