Perhaps the most obvious difference is the mains power, at 220 V or 240 V or whatever the standard is. It turns out that for most computer equipment, the power brick will accept either voltage and you just need to buy a replacement mains power cable with a New Zealand plug on one end and whatever your computer equipment needs on the other. So far I've used this with the D-shaped PC power cable, the "cloverleaf" three-lead plug for the Mac Mini and some other device, and a two-lead cable for things like my external USB hard drive.
We got home broadband from Xtra, which is the internet arm of Telecom, the largest and until fairly recently the only phone provider in New Zealand. They provide DSL service at varying service levels. The one we chose gives us 3.5 Mbps down, 128 kbps up, and a total data transfer of 5 GB per month, for $50/mo. It remains to be seen whether our monthly usage will fall under this threshold. If we go over, then we'll be reduced to dialup speed for the remainder of the month. You can get up to 10 GB this way, but once you want more data transfer per month then you get to pay overages of 2c/MB. The max plan with Xtra is 3.5 Mbps down, 512 kbps up, 40 GB/mo, 2c/MB overage, for $150/mo. Ouch.
The television standard here is PAL instead of NTSC, but apparently every reasonably advanced TV you can buy here accepts both PAL and NTSC inputs. This is important for playing DVDs, because the video signal on the DVD is encoded in either PAL or NTSC. We got a TV that supports both standards, and a DVD player that is region-free (actually it came with instructions on how to change the region from the default of 4, to accept any DVD region). So now we can play DVDs that we brought with us, as well as rented ones from the video store down the street.
I got a Linksys WRT54G v5 wireless router, but for some reason I'm having a problem where the router loses the internal network after about half an hour of use. This appears to affect both wired and wireless connections. Cycling the power on the router fixes this, but I'm going to have to figure out what the real problem is. I've already checked the firmware version and it's the latest. Anybody heard of this kind of problem? Any ideas on what to try? I may end up taking it back and getting a different one, and hope it's a problem specific to this unit.