The main difference: two zodiacs
Vedic and Western astrology both use a 12-sign zodiac and share much of their planetary symbolism. They measure the zodiac differently, and that one difference leads to most of the others.
Western astrology uses the tropical zodiac, which is fixed to the seasons. Zero degrees Aries begins at the spring equinox (around 21 March), wherever the stars happen to be. The signs follow the Sun's seasonal position relative to Earth.
Vedic astrology uses the sidereal zodiac, which is fixed to the stars. Zero degrees Aries is a set point against the background stars. In the Lahiri ayanamsha, the most widely used standard in India, that point is set by the star Spica (Chitra nakshatra), which sits at the start of Libra.
Because of the precession of the equinoxes, the two zodiacs slowly drift apart. Today the gap is about 24 degrees, close to one full sign. That is why, for most people, the Vedic Sun sign is the sign before their Western one.
Sun sign and Moon sign
In Western astrology your Sun sign is your main identity marker. Someone who says "I'm a Scorpio" means the Sun was in Scorpio at their birth.
In Vedic astrology the main marker is the Moon sign (Janma Rashi). The Moon rules the mind, emotions, instincts and the texture of daily life. Horoscopes, transit readings and techniques like Sade Sati are all read from the Moon sign.
Vedic astrology also gives great weight to the Lagna (Ascendant), the sign rising on the eastern horizon at the moment of birth. The Lagna fixes the whole house structure and shapes the body, the personality and how you appear to others. A full Vedic reading looks at the Sun, the Moon and the Lagna together: the Sun for purpose, the Moon for the mind, the Lagna for how you meet the world.
The Dasha system
The biggest practical difference is the Vimshottari Dasha system, a 120-year cycle of planetary periods laid over the birth chart. It shows when each planet's themes become active in your life.
Everyone moves through a sequence of Mahadasha (major period) lords, and each period lasts between 6 and 20 years. Dashas let a Vedic astrologer say when a placement in the chart is likely to show up, in addition to what it suggests.
Mainstream Western astrology has no direct equivalent. It times events with progressions, solar returns and transits. These are valid tools, though none of them gives a long, fixed sequence of periods the way the Dasha does.
Nakshatras: the 27 lunar mansions
Vedic astrology divides the zodiac into 27 Nakshatras of about 13 degrees 20 minutes each. The Nakshatra the Moon was in at your birth, your Janma Nakshatra, affects personality, compatibility, Dasha timing and spiritual nature.
Nakshatras add detail that the 12 signs cannot. Two people can share a Moon sign and have different Nakshatras, and the difference in their temperament and timing can be large.
Planets and dignity
Both systems use the seven visible planets, from the Sun to Saturn. Vedic astrology also treats Rahu and Ketu, the lunar nodes, as grahas that give results through their sign and house, and they play a central part in timing. Western astrology uses the nodes too, though in a smaller role. The modern outer planets, Uranus, Neptune and Pluto, are not traditionally used in Vedic astrology.
The Vedic system also sets out planetary dignity in more detail: exaltation, debilitation, own sign, and friend and enemy relationships. This lets an astrologer judge how well a planet can deliver what it promises in a given chart.
Which one should you use?
Both systems are consistent within themselves, and both have helped people for centuries. Vedic astrology is strongest on timing and on karmic patterns, thanks to the Dasha system. Western astrology has built rich frameworks for psychology and personal growth.
If you want your karmic pattern, the timing of major life events and the spiritual side of your chart, set within the Indian tradition, Vedic astrology covers all of that in one system. You can see how it works on your own chart by generating a free Kundli.