Time of year you travel to Antarctica does make a difference, but deciding which time of year is "best" depends on what you are looking at getting out of your Antarctica adventure. Specific wildlife sightings - mating season - new hatchlings - weather - icescapes - mud - penguins poo smell at its worst/best...?
These two images are a good way to visually compare. Both pictures are taken at the Aitcho Island; the first is from November, and the second is from February.
December to Early February: December and January have the most sunlight (up to 20 hours a day) and daily temperatures are at their warmest. In January, temperatures at the Peninsula average 34 Fahrenheit. Penguins begin hatching and wildlife, especially penguin chicks, is most plentiful during this time typically.
Mid-February and March: Late summer, February and early March is the best time to spot whales, though you are taking the risk that other wildlife may already be gone out to sea. By March, the chicks are quite large, and start to fledge. Weather wise, temperatures are beginning to drop as the season starts to change. Daily highs -- average roughly 29 Fahrenheit at the Peninsula. There tend to be less vessels operating at this time, which means you won't have to compete with other ships for landings. This time of year you are also likely to have better access to areas further south as polar ice melts. Also, you will rarely walk on snow during this time; expect rocky and muddy landings.