A DSLR (just as a SLR) uses focus sensors instead of the image sensor to do focusing and focus tracking.

Typically the focus sensors are placed below the mirror, and the mirror is semi-transparent to let some light through to the focus sensors, and small mirrors on the back of the mirror direct the light to the sensors.

                  \
                   \
Focus mirrors ->   /\--------------------- <- incoming light
                   | \
                   | /\
                   |   \
                   |   /\
                   |     \
                   |      \
Focus sensors ->   * * *

This means that a DSLR has a lot fewer focus points that a MILC, so it can have some difficulties to focus on a small object.

On the other hand the focus sensors have sensors at different heights so that they can determine in a single reading approximately where the correct focus is. Using the image sensor means that you have to take two readings with a change of focus in between to get an idea of where the correct focus is, so a DSLR has the potential to be a bit faster to focus.

There are of course several other factors that affect the focusing speed, like how much light the lens lets through, and the speed of the focus motor. It's hard to make a fair comparison between two cameras where all those factors are different.