I have every fighter ship fully engineered, from the smallest to the biggest. Never did pvp so I can only speak for pve.
The small ones, viper, eagles, are about flying skill. The fight becomes about flying a combination of FA off and on, matching the opponents speed and staying behind them. Once you can do that (I still fail sometimes) you can kill any npc ship, but it takes more time of course. Often I don't even care about the kill,I just play hide and seek. Favorite is Viper 3.
Then the medium category is Vulture by itself. Still handles great, but can kill anything pretty fast. Probably my most fun fighting ship in the game, and favorite of all.
Then the medium/bigger ones, Fas, Chieftain, Fdl (probably the best here), fire power becomes more important and flying less, you can even tank anything. I like the Gunship despite not being great, cause of the fighter pilot immersion. I have one with torpedoes, love the one shot challenge of doing wing assassination missions by myself, hit and run style!
Big ones, I like the Corvette, better movement than the others, brings in the numbers. My BGS one is close to 5 billions in bounties, if they bring the Odyseey crime system in Horizons I'm in trouble!
It's important to match engineering with your guns of choice, and fighting style in all ships. Be it heat management, power, shield or hull maxing out, etc, there's lots of styles one can take a ship to. Do you like to evade or fight head on? Shield or hull tank, fixed or gimballed weapons, etc..
I setup different ships for different roles. One for assassination missions, one for combat zones, one for skillful flying, etc,etc.. Endless combinations. That's what I do in Elite really when I play with a purpose..