With early 2013 cameras, it's generally accepted that using contrast detection autofocus on SLRs (ie live view on most SLRs) is something which is really suitable only for static, or close to static, subjects due to the slow focusing speed. On the other hand, the current best of breed mirrorless cameras (the Olympus OM-D E-M5 often being quoted here) have autofocus systems which are significantly quicker at achieving a focus lock, if not quite being up to the performance of phase detection autofocus systems.
My understanding is that both systems are using the same technology, so why is it the case that mirrorless cameras have much quicker autofocus systems than SLRs in Live View mode? Is it the case that the lenses for mirrorless systems are optimized for quick CDAF performance, and if so, what are those optimizations?
Edit: in response to one of the answers, I'm not thinking about how cameras like the Nikon 1 series or the Canon EOS M have quicker autofocus due to the use of phase detection elements in the sensor; I understand how using an entirely different technology will improve things - what I'm interested in here is how some manufacturers have made contrast detection autofocus much quicker than is apparently possible in SLRs. Similar reasoning applies to the Sony SLT series as that's again using PDAF rather than CDAF.