When talking with Witches or Pagans in general, there will always be conflicting information and answers. However, most Witches who follow what is known as the Wheel of the Year, a seasonal calendar with sabbats, or celebrations to mark the changes on earth and celestially speaking through out the year, Samhain is noted as the Witch's New Year. This is due to the Celtic influences on the Wheel of the Year. Samhain is one of the four main sabbats in Celtic culture, one the most commonly attributed cultures to much that falls under the spiritual path of Witchcraft. According to the Celts, a new day began at dusk, not dawn; and a new year began at the beginning of the Dark half of the year, Samhain.
The idea behind this concept comes from the notion that before there was light, there was darkness. Before there was life there was a void. From the darkness, light was born. Thus, a new day begins at the beginning of the dark night. The Celts divided their year into a dark half and light half. The dark half was their winter for 6 months and the light half their summer for 6 months. Samhain falls half way between Fall equinox and the Winter Solstice. The Equinoxes are a time of balance between light and dark, the solstices are the peaks of the Dark time and then the Light time. Half between an equinox and solstice marked the beginning of one half of the Celtic year.
Some witches and traditions hold that Yule should be counted as the Witch's New Year as it is the time when the Sun in reborn again, and begins another cycle of increased light on Earth. It is the time when the God is born as the New Born Sun, and the Goddess hibernates, much as the earth hibernates. This sabbat is not Celtic in origin, but has been celebrated in cultures around the world through out history. While the New Born Sun is an important date to take note of and honor, in terms of modern Witchcraft and use of the Wheel of the Year, Yule marks the end of the hours of darkness being greater than the hours of light in a day, but Winter is still in full swing until after the Spring Equinox. It is a time of great celebration and honoring of the Sun which has at last been renewed and beginning to build strength once more, but we are fully immersed in the Dark half of the year at this time, which was begun back at Samhain.
In the end, you must go with what feels right to you. Search for historical celebrations and ideas around each of these wonderful Sabbats and see what ideas mesh closest to your own, and the Sabbat which feels right to you as the New Year is what you should turn your attention to for that celebration.