That depends on what you want to see or do. Keep in mind that you cannot cruise to the polar regions all year round. Travel is restricted to the polar spring and summer, when daylight lasts between 18 and 24 hours each day.
Antarctica - from October to the beginning of December
The continent is covered in snow to the water’s edge. Penguins build highways as they waddle the same path again and again, from the sea to their nests far from shore. During this period penguins, shags and seabirds court and lay their eggs.
Antarctica- from December through February
The snow retreats, exposing rocky headlands. Penguin chicks hatch and their parents spend endless hours feeding their hungry young.
Antarctica - from mid-February to March
The whales return to feed. Seals haul out on the beachheads and penguins begin to moult. Antarctica is preparing for long months of darkness. Highlights for travelers are whales, red snow and fledging Gentoo Penguins acting like miniature Charlie Chaplins.
The Arctic - from June to mid-July
This is the best time to see ice and snow. The midnight sun has not yet melted the ice, so polar bears and walrus will be hunting on the ice edge. Birds are returning to breed.
The Arctic - from mid-July to mid-August
The best time to circumnavigate Spitsbergen, as ice is less likely to block channels. Tundra flowers are blooming. Wildlife is abundant.
The Arctic - from mid-August to September
The days are shortening; birds begin to migrate south; and skies can be moody.