There were 3,435 dog attacks reported to 72 New Zealand councils in 2001/2. From 1989 to 2001, there were 3119 hospitalizations and one fatality due to dog bites. In the year ending 2003, ACC received 8,677 claims for dog bites requiring medical attention. 
A recent New Zealand study of adults who made claims to ACC for dog bites found that 26 per cent of the bites occurred in a public place and 21 per cent occurred at home, with the remainder divided between other types of private property.  In this study, only 11.6 per cent of dogs were loose and unsupervised in a public place, although other studies have found higher levels than this. Territory defence was the most common reason for a dog to bite, followed by accidental bites due to pain or fear. Pure-bred dogs were responsible for 40 per cent of bites, mixed breeds for 27 per cent and the remainder unknown. The top ﬁ ve pure-bred categories were German Shepherds (8%), Pit Bull Terriers (7%), Rottweillers (6%), Jack Russell Terriers (4%) and Labrador Retrievers (3%).Here's the underlying survey data, though note that this is just on adult survey respondents; folks seem most outraged about attacks on kids.
As pit bull terriers are pretty uncommon and labs are very common, the conditional risk presented by pit bulls is pretty high, although that could easily be due to that scary people who like to abuse dogs and to intimidate people choose that breed; if that breed were banned, scary people would likely converge on another breed pretty quickly. Note also that a reasonable proportion of mixed breed attacks will likely involve Staffie-crosses.
If less than 12% of dog attacks involved dogs running loose, where ownership would be most difficult to pin down under a liability regime, that increases the likely feasibility of a strict liability plus insurance regime over alternatives.
More data: the Department of Internal Affairs's Dog Safety and Control Report:
Looking at dogs by breed and considering only those with more than 500 in the NDD, the highest rate of dangerous dog classifications are for the pure-bred American Pitbull Terrier with 1.9% of 3,469 classified as dangerous. Next are the cross-bred American Pitbull Terrier (1.4% of 3,258) and the Dogue de Bordeaux (1.2% of 599 dogs). All the remaining 126 breeds with 500 or more dogs in the NDD have a dangerous rate less than 1%.This all makes me more confident in my current heuristic: upweight the chances that a dog and its owner are dangerous if the dog is a Pit Bull. That gives no argument for banning Pit Bulls, as scary owners would shift into other dogs - a determined psycho could turn a German Shepherd into a scary attack dog fairly easily.
In terms of actual numbers, the American Pit Bull Terrier pure-bred has the largest number (67) of dangerous dogs in the NDD, followed by the Staffordshire Bull Terrier (48), the American Pit Bull Terrier cross (46), the Labrador Retriever (43) and the German Shepherd (42). Some 352 breeds did not have any dogs classified as dangerous.
And in response to a couple of comments on a prior post: the point of a strict liability regime isn't to ensure compensation to those bitten. It's to ensure that an actuarily fair premium is assessed on owners who are compelled to buy liability insurance as part of dog ownership so that owners who pose too great a risk are priced out of the market. But as liability insurance isn't even mandatory for car ownership, I'm less than optimistic about the chances for it in dog ownership.
HT on all of this: Wayne Heerdegen, who spent a bit of time at Treasury working on dog policy.