There are no differences between the 4 port Mayflash gamecube adapter and the Official Wii U gamecube adapter on the PC. They work exactly the same. The Mayflash adapter does have a PC mode but that is to use the controller as a third party controller for other programs. For dolphin its best to use the Wii U mode as there is no lag and it polls inputs in as if it were a real console. The 2 port adapters are ass though and I really do not recommend them at all
Windows 10 x64 | Intel Core i7 4790K @ 4.4ghz | NVIDIA GeForce GTX 1070| 16GB DDR3-2400 | Bose Companion 5 | Sennheiser Momentum 2.0| Logitech G502 Proteus Spectrum
MacBook Pro Retina 15in 2014 | OS X El Capitan 10.11 | Core i7 4770HQ| Intel Iris Pro HD Graphics | 16GB-DDR3-1600