A commenter suggested that the mirrorless Olympus OM-D E-M5 can’t be as good as a DSLR because it can’t possibly focus as fast.
Actually, Olympus claims that they have achieved the world’s fastest autofocus speed with the E-M5. Maybe there’s an asterisk in there somewhere, but the camera’s “Single AF” speed is probably faster than any DSLR in the same price range. (You should look at real camera review sites for actual focus-speed measurements.)
For some background here, autofocus DSLRs use phase detection autofocus (PDAF), which uses different areas within the lens to create a rangefinder which can determine how much out of phase the high-contrast areas in the focusing area are off, and move the lens exactly the correct amount to put it into focus.
Contrast detection autofocus (CDAF) is a more iterative process which focuses the lens the way a human would, which is to move the lens around until the focus area is as sharp (highest contrast) as possible. This is the focus method used on all non-DSLR autofocus digital cameras, and yes, traditionally it has been a lot slower. But thanks to Moore’s law, the computing power now exists to read out the sensor, determine contrast in multiple areas of the image, move the lens, and then do it over and over again, all in just a fraction of a second.
The advantage of CDAF is that it’s more accurate because it doesn’t depend on the precise calibration of the lens and the PDAF mechanism. CDAF uses the same sensor that records the image to determine sharpest focus. Online photography forums are full of complaints from people having focusing problems with their DSLR systems, especially when they use wide-aperture lenses. This generally doesn’t happen with CDAF-based focusing systems.
CDAF also allows other neat tricks. For example, there’s a face-detect mode in which the camera is able to identify a face and focus on the eyes. And the E-M5 has a touchscreen display; just touch the display where you want to focus, and the camera will focus there and take a picture.
But PDAF still retains an advantage with 3D focus tracking, because PDAF is an inherently three-dimensional measurement. However, most inexpensive DSLRs lack enough focus points to have quality 3D focus tracking. I see PDAF becoming a niche thing for people photographing sports, with CDAF being becoming the preferred choice for regular photography because of its better accuracy and other features.