BIF shots on mirrorless cameras are very challenging for me even with the recent advance in technology. The track speed is still lagging behind a good DSLR.
Canon 5D MKII, EF 24-105mm f/4L, EF 50mm f/1.8, EF 100mm f/2.8L Macro, Tamron 70-300mm f/4.0-5.6 SP Di VC USD XLD, Sigma DG 150-500mm f/5.-6.3 APO HSM.
Canon EOS T3i, 7D and 70D EF 17-40mm f/4L, EF-S 55-250mm f/4-5.6, Sigma 18-250mm f/3.5-6.3 DC OS HSM, 430 EXII Flash.
Sony A200, SLT-A58 System with HVL-F42AM Flash.
Mirrorless APS-C camera: Samsung NX100, Canon EOS-M.
M4/3 systems: Olympus OM-D-E-M5 and Panasonic DMC-G3.