Gambatte was originally written by sinamas, however the core has since been rebased on Gambatte-Speedrun which has focused on extreme attention to accuracy with the Game Boy Player, the most commonly used platform for speedrunning Game Boy games and also the most accessible platform for console verification of GB/GBC titles.
See this page for detailed information on GB sync settings including configuration of the GBA platform and BIOS for console verification.
Super Gameboy is available and implemented using the bsnes core see SNESHawk. However, it is by far the least maintained of the GB cores and is missing a significant amount of accuracy improvements to bsnes + SameBoy.
New C# core written from scratch by Alyosha. Features comparable/improved accuracy and increased peripheral/mapper support over gambatte, but runs significantly slower at uncapped framerate.