While a DIY solution would probably be slightly cheaper, and possibly easier to work bugs out of, the dedicated boxes are usually smaller, take less power, and have enough adequate cooling to sufficiently keep the drives from cooking. This means that there is less noise. Notice I did not say less heat; that's dependent on drive selection, quantity, and the design of the box overall.
I haven't had a need to look at NAS for personal use, yet.... but maybe sometime soon I will.
One overlooked thing are the drives; I recommend enterprise level drives; they should be built better, and last somewhat longer, as well as have supportive features for raid controllers.
I'm a WD guy through and through, and I would get either RE4's or the new Red series. Personally, I'd get the RE4's. If you feel a bit spendier, you can get SSD's as well, but honestly, unless time is of the absolute essence (which in your home, I think data accessibility, reliable reads, and data integrity are more important), mech drives are still cheaper and still plenty reliable. Not to mention, to me, some SSD's seem inconsistent with performance, as well as the ability to do really strange things. Samsung 840 Pro secure erase anyone? No thanks, I've never had a mech drive fail from just erasing it, but I have had them fail when they were hit with a sledgehammer while running
