It might take a little reworking of your photo settings and techniques to get the most from the NEX6...it's not going to match a good DSLR in every respect, such as tracking focus on a moving subject - but it can certainly acquire focus as quickly and accurately once you figure out the best settings and the best technique. ; As someone who has been shooting side-by-side DSLR and NEX for a few years now, I can tell you that I am at the point where I can focus anything, anytime, accurately and quickly with the NEX, as fast as I can with the DSLR...the only thing I can't do as well is use continuous autofocus and have it track a subject coming quickly at me...which I think would even be challenging on the NEX6 with PDAF on sensor - there's still not quite a substitute for big, dedicated PDAF sensors in a DSLR.
A few things I find on the NEX that seem to help it...first and foremost, turn off the AF assist light if you haven't already. ; Noone can really explain why, but it seriously slows down the focus especially in low light where it hunts and hunts. ; With it off, my low light focusing is much faster. ; Second, use the spot focus point most of the time - it's the most accurate, and the most reliable, and usually the fastest. ; Keep the camera in AF-S mode, rather than continuous focus...even for moving subjects - you can always cycle the shutter button as needed to refocus a moving subject. ; There's a little bit of 'P&S' focus technique required with the mirrorless cameras - whereby you 'feed' a good contrast focus area to the spot focus point, then quickly recompose before shooting. ; Dedicated PDAF seems to lock on easier in lower light, whereas CDAF needs some decent contrast or pattern...so if shooting a person standing in a darkish room, use their hairline, eyebrow, collar, or shirt pattern to focus on and recompose. ; Look for light glints, vertical or diagonal lines, etc as the best places to focus on, as long as they are the right focal distance as your subject - then recompose and shoot.
I really push my NEX focus system in very challenging conditions - birding in heavy shadow and mixed light, with long telephoto reach of 350mm+, through branches and clutter, with the bird often in shadow and partially blocked, and moving every few seconds...yet after getting used to handling my NEX a little differently from my DSLR, and using those settings I mentioned, I pretty much don't get missed focus anymore, and focus times are in the fractions of a second...I have no fear using the NEX instead of the DSLR for these types of shots - almost any shot, to be honest, though I know some situations like birds-in-flight or sports action where I need to pan and continuously focus, I know I'll need to work harder to get decent results and likely see a lower hit rate than the DSLR.
That said, I can't say the NEX replaces a DSLR for me - I still shoot with both - it may be that you end up preferring a two-camera system...DSLR for the more demanding focus needs or fast subjects, and NEX for lighter weight and travel and normal photography needs. ; But try a few changes with the NEX, and see if a slightly different approach helps improve your focus speeds and reliability...it's very common on the NEX forum to see complaints of regularly missed focus and slow focus, yet there are almost equal numbers that seem to not suffer this problem at all - which tells me that it's mostly down to the photographer and the settings...it requires a little more attention and just right settings to work at its best.
