I disagree with lordbusiness - disregarding focusing time (as previous poster said, "half-press" the shutter first), EVIL/mirrorless cameras are going to be faster than SLRs unless incompetently engineered.
There are outliers like the NEX-5 which had a shutter lag of over 100ms, even when pre-focused, but the modern mirrorless equivalents of the 7D achieve less shutter lag.
A DSLR has the intrinsic problem of having to wait for the mirror to move out of the way before the image can be captured. The mirror mechanism's speed is limited by the strength and flexibility of its materials (too fast and it'll break), and the power level of the actuator moving it. Not to mention the faster you move the mirror the more slap you will get, causing vibrations in the camera that affect image quality. There is a "limit of physics and material science" problem inherent in SLRs.
A mirrorless camera has none of these disadvantages - and it shows, even the vaunted Canon 1D has a shutter lag between 40-50ms depending on model, while the Sony NEX-5N has a shutter lag of 22ms.
The Canon 7D lordbusiness brings up clocks in at ~70ms. In fact none of Canon's DSLRs can get below 40ms.
The Olympus E-M1 comes in at 50ms, as is the Fuji X-T1. Mirrorlesses already outperform even high-end DSLRs when it comes to shutter lag. And they will continue to get faster as more mirrorlesses move to electronic instead of mechanical shutters.