in one on one, big will beat small, always. however if its mass to mass, small ships will always beat big ships.
also small ships are very effective at exploiting a hole in a big ships armour, because you can get very close and shoot the systems.
also I prefer to use a small ship if I am going to explore the universe (expecting to PVE, or PVP if multiplayer) because A. I like them and I use them like a house lol B. pew pew pew, instead of pew pew C. generally much faster than a capital ship D. can easily dodge missiles, even swarmers. E. I can land on planets and hide.
why fight when you can mess with their minds? be everywhere at once, yet nowhere. shoot off all their cameras and turrets without them noticing too much. the look on their face when they find out that their capital was nearly taken out by a 237 mass fighter, and they then realise that you have been tailing them for two hours and have taken out all of their turrets and have engraved your faction emblem onto the side of their ship. that is why I like small ships.