Many newer mirrorless cameras feature much faster contrast-based AF systems (due at least in part to much quicker read rates), and have actually caught up to phase-detection DSLRs in AF speed. In any event, for still subjects in good light, at least, today's mirrorless interchangeable-lens cameras can hold their own against the best DSLRs, and are way better than the compact digital cameras—and the contrast-based AF systems employed by DSLRs in live-view/movie mode.
LENSESBecause many DSLRs are able to use the same lenses as the manufacturer's 35mm SLRs, most offer a wide range of lenses. Newer lenses are designed specifically for digital imaging, and tend to produce better results. Even the relatively new Four Thirds System provides a wide range of lenses.
Mirrorless camera systems are newer, and thus don't yet have such extensive lens lineups. But all the basic ones are there, and the mirrorless models offer an advantage over the DSLRs: Because the mirrorless models have much smaller "flange-back" distances (the distance between the lens mount and the image plane), they can use any lens for which an adapter is available. Many mirrorless camera users employ such mounts to attach Leica, Zeiss and other top lenses (although this means losing autofocusing capability).
Sony offers the LA-EA2 adapter for its newer NEX cameras. This incorporates a phase-detection AF system similar to the one in their SLT cameras, and not only permits mounting Sony (and legacy Minolta Maxxum) DSLR lenses, but provides phase-detection autofocusing with them.
One point to bear in mind is that you get DSLR image quality by using DSLR-sized image sensors. And while manufacturers have done an amazing job of squeezing big DSLR sensors into truly compact bodies, a given-sized sensor requires a given-sized lens diameter to produce an image circle sufficiently large to cover the format. Thus, while the mirrorless interchangeable-lens cameras with the largest sensors produce the best image quality, they also have the largest lenses. But the overall body/lens package is still much smaller than an APS-C (or even Four Thirds System) DSLR with equivalent focal lengths—even though it won't fit in a pocket.