Capsicum and chilli are closely related and share almost identical growing requirements: both need a long, warm, frost-free season to fruit well, which makes them noticeably more region-dependent than most other summer vegetables.
In Auckland and the Bay of Plenty, both can be planted outdoors from September through December. In Waikato and Wellington, the window narrows to October-November. In Canterbury, plant in November only, once the season has properly warmed up. In Otago, neither crop has a reliable outdoor planting window at all. The growing season there isn't consistently warm or long enough for capsicum or chilli to fruit well outdoors. Otago gardeners are better off growing both in containers or under glass, where they can control temperature and extend the season artificially, rather than planting them directly in the garden.
Both need full sun and space to grow. Capsicum plants are typically spaced around 45cm apart, chilli slightly closer at 40cm. A capsicum plant will usually produce 4-8 fruit over a season; chilli plants are far more prolific, often producing 20-40 fruit each. Both take a while to get there: 90-110 days to harvest for capsicum, and anywhere from 85-120 days for chilli depending on variety.
chilli plants are far more prolific, often producing 20-40 fruit each.
Verticillium wilt and blossom end rot are the main diseases for capsicum; chilli is a bit more disease-resistant but still susceptible to verticillium wilt. Aphids, whitefly and thrips affect both. Good companions include basil, tomatoes, onions and carrots. Both share tomato's dislike of being planted near brassicas or fennel.
If you're gardening in a cooler climate and don't want to give up on capsicum or chilli altogether, grow them in a large pot instead. Move it to the warmest, most sheltered spot in the garden, or bring it under cover on cold nights. That's the standard workaround, and it's genuinely the more reliable approach south of Canterbury.