The Paksha is based on the cycle of the moon:
The first 15 days when the moon is waxing which is the bright fortnight is called the Shukla paksha. The 15 days when the moon is waning, the dark fortnight is called the Krishna paksha.
Generally the Shukla paksha is more auspicious for certain things. In the Chandi, the Goddess specifies that the 8th, 9th, and 14th days are the most auspicious for listening to or reciting her glories. This could be either paksha. The 4th day is auspicious for Ganesha. The 11th day is auspicious for Vishnu, called ekadashi. The 14th is auspicious for Shiva and the night of no moon called Amavasya is auspicious for Kali. And of course there is the full moon or Purnima.
The Ayana is based on the cycle of Sun:
Uttarayana is the period covering the north-ward journey of the sun i.e. north ward passage and it consists of winter, spring, and summer. It is the period from winter solistice to summer solstice. The period starts from Sun's entry in to Capricornus ( Sayana Makara) on December 21.
Six months of Uttarayana of ours is the day time for Devas.
So Uttarayana is more auspicious than Dakshanayana,
Dakshanayana :- It is the period from Summer solstice to winter solstice i.e. south ward passage of the sun and it consists of Rains, Autumn , and Hemanta . the period starts from Sun's entry in to cancer ( Sayana Karkata) on June 21. At summer solstice day , the day is longest and at winter solostice , the day is shortest for observers in the northern hemisphere.
Six months of Uttarayana of ours is the Night time for Devas.
( Our one year is one day for Devas)
The Hindu calendar is a combined lunar and solar calendar. It is based on the position of both sun and moon. When referring to the lunar cycle we refer to tithi and paksha, but when referring to the solar cycle we talk in terms of sankranti and gate. Festivals and other religious occasions are based both on the solar and the lunar cycles.