Quick answer
The south coast, Funchal, Câmara de Lobos, Calheta, Ponta do Sol, is the sunniest, driest and warmest part of the island year-round, sheltered by the central mountains from the north-east trades. The north coast (Porto Moniz, Seixal, São Vicente) is greener, cooler and far wetter.
Context
The mountainous spine running east–west through Madeira creates a permanent climatic split. North-east trade winds hit the northern slopes first, dropping most of their moisture there. The south then sits in a rain shadow with significantly more sunshine and a sea-tempered, almost Mediterranean climate.
Ponta do Sol regularly tops Portugal's monthly sunshine charts. Funchal averages 7 hours of sun a day year-round. Across the ridge, São Vicente sees 150+ rainy days a year and afternoon cloud.
If your trip priority is reliable beach weather, base on the south coast. If it's hiking and waterfalls, the north coast scenery rewards the wetter weather.