It is slower than a typical DSLR with PDAF when it comes to low light - the on-sensor PDAF no longer works once you get down to about 2EV at the metering point, so as light gets lower overall, the camera switches to CDAF to focus - in my experience it actually handles focusing very well in low light, a touch better than my NEX-5N, and always accurately and does acquire even in very low light, but it is slower to do so. I'd say where my DSLR can get near-instant focus at something around 1/20th of a second at ISO6400, F1.8, and 1/30 shutter, my A6000 with the same settings in the same light conditions may take as long as 1/3 to 1/2 second to acquire focus. That's without any AF assist lights and no flash. But it does still get the focus correct - and it's up to what you need to shoot in low light as to whether the roughly 1/3 second is considered "much slower", or just a little slower. Someone shooting a running football player at 200mm in low light and needing instant focus may find that 1/3 second delay to be interminable - someone shooting a person sitting in a dark bar, or an object on the table, isn't likely going to be perturbed waiting 1/3 second longer.
I shoot fairly extensively in low light - I'm often at ISO6400 to 12800, shooting wide open at F1.4 or F1.8, and getting shutter speeds of 1/15 to 1/40...I've not yet had the A6000 be incapable of getting proper AF, but just a bit slower than my DSLR can.
Sony DSLR-A68 / Sony 18-250mm / Minolta 50mm F1.7 / Tamron 150-600mm / Minolta 300mm F4 APO
Sony A6300 / 18-55mm F3.5-5.6 / 55-210mm F4-6.3 / 10-18mm F4 / 35mm F1.8 / 16mm F2.8 / FE70-200mm F4 G OSS / FE70-300mm F4.5-5.6 G OSS / via manual adapter, lots of Pentax K mount, Konica K/AR mount, and Leica M mount manual lenses