Neither the LCP nor the Bersa is a finicky gun in my experience.
My LCP has run several different brands of JHP, including Aguila and Magtech.
As for what works best on a criminal, I haven't checked, I buy what's available and will run in my guns, at least these days.
Generally the modern bullet designs should work well, so much effort has been put into them: Speer Gold Dot, Winchester PDX, Hornady Critical Defense and Critical Duty (more penetration)....
I have actually had problems with Cor Bon functioning in several guns in recent years, even my LCP.