The most important difference between Vedic and Western lies in the choice of Zodiac. In Western astrology, the Tropical Zodiac is used while Vedic astrologers use the Sidereal Zodiac. Western astrology uses planets in signs extensively, but Vedic astrology uses signs in a different manner.
The House System
Modern Western astrologers mostly use one of the many house systems in which the degree of the Ascendant is placed as the beginning of the First House, with either equally- or unequally-sized houses. Vedic astrologers, however, use Whole Sign Houses. The Ascendant can come anywhere in the First House, and each house comprises only one sign. Many also tend to use Bhava/Shri Pati houses for a part of their work.
Rulerships of Planets and Signs
Western astrologers use all the major planets, including Uranus, Pluto, and Neptune. They also attribute rulership of Aquarius to Uranus, Scorpio to Pluto and Pisces to Neptune. However, Vedic astrologers use the visible planets, and they attribute rulership of Aquarius to Saturn, Scorpio to Mars, and Pisces to Jupiter.
Aspects, Aspect Patterns Orbs & Chart Shape
Western astrologers use several aspects, including the five Ptolemaic aspects (sextile, conjunction, trine, square, and opposition). Planets aspect other planets as well as the angles (Ascendant and Midheaven).
Vedic astrologers take a different approach. In their system, each planet associates with all planets in the same house. It also aspects the opposite house and the planets in that house. Saturn, Mars, and Jupiter also have additional aspects to both houses and planets.
Methodology and Approaches - Strengths and Weaknesses of Planets
Western astrology considers retrograde planets as weak, but in Vedic astrology, they are seen as strong (because retrograde planets are close to the earth, and therefore larger and brighter).
Modern Western astrologers rarely use the concept of combustion (planets near the Sun), but to Vedic astrologers, this is a fundamental principle. They believe a planet to be weak when it's within 6 degrees of the Sun (and very weak if it's within 3 degrees of the Sun).
According to Vedic astrologers, true planets (Mercury through Saturn) that are within one degree of each other are at war, and this is seen as a major weakness. Western astrology does not subscribe to this.
If a planet occupies the same sign both in the natal chart and the Navamsha chart (unless it's debilitated), this gives the planet strength, (in Vedic astrology), but this is not used in Western astrology.
In Vedic astrology, planets get Dig Bala (directional strength) when they occupy specific angles: Moon and Venus in the 4th, Jupiter & Mercury in the 1st, Saturn in the 7th and Sun & Mars in the 10th. This concept is not used by Western astrologers.
All Vedic astrologers and some western astrologers use Mutual reception. The former call it a Parivartana yoga, and it has many meanings, including strengthening planets in both the divisional and divisional charts.
Western astrology sees Saturn as challenging. However, Vedic astrology uses the concept of benefic and malefic planets to a much greater extent. For example, Mercury is benefic unless it is solely under the influence of other malefic planets. Unless it is within 72 degrees of the Sun, the Moon is benefic. Venus and Jupiter are always benefic, while Mars, Sun, Saturn, and the Nodes are malefics.
Western astrologers use Transits, especially by the outer planets, as the main predictive device. However, some use progressions and/or directions as well. Vedic astrologers depend on the Vimshottari Dasa system (cycles and sub-cycles wherein particular natal planets become activated) and also use the transits of Jupiter and Saturn (but not the transits by Pluto, Neptune, and Uranus). Some may also use other Dasa systems.
Lunar Mansions and Harmonic charts
It is very rare for Western astrologers to use lunar mansions, but Vedic astrologers do use them. They call them Nakshatras and use them for Dasa calculation, natal work, and electional astrology (Muhurta). Using Nakshatras for Muhurta probably preceded the use of the 12 signs in astrology.
Western astrologers do not often use harmonic charts. These are called Varga or Divisional charts in Vedic astrology and are deemed essential to a natal and predictive analysis by Vedic astrologers.
Analyzing Compatibility
Western astrology has many methods to analyze compatibility. This includes looking at the placement of planets in each other's houses, inter-aspects (between charts) and a variety of combined charts. In Vedic astrology, compatibility is assessed by examining the two people's Moon positions and the Lunar attributes. Also, the Navamsha chart is used both to assess the partner and in the timing of relationships.
Western astrologers tend to add the comet Chiron and the four major asteroids to charts, apart from the Part of Fortune.