I've only been able to reproduce your large vs. small weapon tests when I didn't use any utility slots except energy on my ships. If I use a sensible amount of defenses the small weapons win, and they win solidly. How were your ships outfitted when doing these tests?
20x Destroyer, 1 large xray laser, 2x small xray laser, sufficient anti-matter reactors to fit all the guns, crystal forged armor in the rest. advanced evasion computer, tier 4 engines.
20x Destroyer, same as above except all small xray lasers.
Large weapons do win sometimes in large fleet engagements, if they manage to quickly kill one of the earlier ships during the starting phase when they have range advantage. It's still a majority of small wins in ~10 tests.
Are you testing 1v1? I'm only testing reasonable sized fleet engagements.
And I made a separate thread about this, but might as well post it here. Accuracy and evasion are additive, meaning a weapon with 76% hitrate against a 60 evasion ship doesn't hit 0.76*0.6=46% of the time as might be expected but just 0.76-0.6=16% of the time. This is a big part of why evasion is so good.
So how was I getting 40% hitrates against 60% evasion corvettes with weapons that have less than 80% accuracy?
Also having a hard time reproducing getting anything to beat corvettes. I use stormfire autocannons and a PD with 3 HP plating in utility (best engines and defensive computer) and that build beats anything I make.
Are you using equivalent mineral cost and significant fleet sizes?
Try using the build I made for the cruiser above and replace lasers with autocannons.