Both are correct.

Having said that, lemme explain further from a book that I have. There are basically two main differences in the tww systems:
(1) Ayanamsha
Western astrology orients the zodiac to the point of the vernal equinox, which it marks as the beginning of Aries. Thus, its Earth-Sun relationship remains constant (as in the equinoxes). It shows how the planets distribute the solar force i.e. the solar side of our character (that which appears to the world at large)
The Vedic system orients itself towards the galactic centre and thus, it also considers the millennial rotation of the solar system through the precession cycle. Its signs are the stellar constellations. Ayanamsha measures the precession of the equinoxes.
When a Western astrologer says that the sun is in Aries, he does not mean that the sun is in the constellation of Aries; in fact, he knows that the sun is probably in the fixed star of pisces but what he means is that the Sun is in the first of a twelvefold division of the zodiac based on the position of the sun at the vernal equinox.
When a Vedic astrologer says that the Sun is in Aries, he means the fixed star of Aries and not the tropical division which, he knows, is probably Taurus.
Though both of them use the same terms, they refer to different portions of the sky based upon two different ways of dividing the heavens.
(2) Determination of house
The main difference is in the interpretation of the house cusps. Both systems agree that planets located at or near the cusps are strong. However, while the Western system makes the cusp the beginning of the house, in the Vedic system a cusp is the middle of the house. Thus, the 1st house in Vedic will contain half the 12th house of the Western system.
The difference, however, is not as major as it appears. The Western system gives an orb of at least 5 deg to the cusp of a house and sometimes upto 10 deg for the luminaries (Sun and Moon). Planets located these degrees prior to the cusp, though technically in the previous house, are regarded as influencing the house through their conjunction with the cusp.