What DSLR? That might affect the recommendation of DSLM.
The modern DSLM generally grab (acquire) focus very, very quickly. With the possible exception of Fuji. If you require continuous AF, however, the A6000 is a good choice among DSLM cameras, as would be the Lumix GH4 if your budget goes that high.
This link to an in-the-field practical comparison might help you decide, but does not include the E-M10, instead it has the E-M1, which I assume is superior.