Part of the problem with turning battles could be how you are flying. I remember when I first played this game as a kid (when it first came out), I always got stuck in a 1v1 with the AI where I'd constantly be turning, and I would fly n circles for a minute or two unable to get the enemy in my gunsights. The culprit? Flying at full throttle all the time. When I came back to the game after discovering FSO, I learned that decelerating allows you to turn much faster to put a quick end to these sorts of battles.
Also, increasing game difficulty drastically makes the game harder, though some of it is artificial (realistic?) difficulty. Keep in mind that in any setting below insane, your fighter has plot armor and everyone else is nerfed. Enemies (and friendlies) shoot slower than their weapons' maximal fire rate, cannot turn at their ship's maximum turn speed, capital ships cannot shoot from more than 3 turrets at a time, and your fighter has craploads more shields/hull/energy. Turning up difficulty gradually removes these handicaps, with insane removing all restrictions on enemies and all benefits for yourself (realism mode). The downside is that insane enemies will almost never miss a non-accelerating target, since their shots always land on the lead indicator. This can actually an advantage, because you're nearly impossible to hit if you keep your own acceleration, whether it be from engine speed or turning, high at all times, though you tend to vaporize in 1-2 seconds if you mess up. This is where good maneuverability and top speed come in: in something that's slow, you'll never have the acceleration to dodge incoming shots, so you tank everything sent your way, which invariably ends up in a quick death. In something fast, you are invincible, assuming you have the skill to never fly into where your lead indicator points.
However, from what I've seen at insane, wingmen can still occasionally be retarded with collisions. The worst offender is still the c37, where you order people onto your wing. That collision behavior never goes away with higher difficulty. That being said, I've never witnessed any fighters colliding into each other during dogfights on insane difficulty, probably because everyone is more agile, and things die so much faster. A notable example is Lion at the Door, which is an exceedingly easy mission on insane because your wingmen will effortlessly kill everything in seconds if you micro them properly, so there isn't time for drawn out turning battles.
tl;dr: Increasing difficulty makes enemies and friendlies much more agile, able to shoot faster and better, and overall, a much bigger threat. However, it also increases artificial difficulty as AI resembles an aimbot at insane. Caveat: increasing difficulty and AI smartness doesn't improve their collision avoidance behavior. However, because they're more agile, they'll collide less in real game situations.