Western or Vedic: which one is actually right?

Someone tells you that you are a Leo. A Vedic astrologer tells you that you are a Cancer. Both are reading the same sky at the same instant, and both are calculating correctly.

What are they actually measuring?

The tropical zodiac begins at the spring equinox, the moment the Sun crosses the celestial equator going north. Zero degrees Aries is defined as that point, and the twelve signs are twelve equal slices of the year that follows it.

The sidereal zodiac begins from a fixed reference among the stars. Zero degrees Aries is anchored to the constellations rather than to the seasons.

Why do they drift apart?

The Earth wobbles on its axis, one full circuit in roughly 25,800 years. The equinox therefore slides backwards against the constellations at about one degree every 72 years. This is precession, it is measured, and it is not in dispute between the two systems.

Two thousand years ago the two zodiacs very nearly coincided. They are now about 24 degrees apart, which is most of a sign.

So which one is correct?

The question does not have the shape people expect. Asking whether the tropical zodiac is correct is like asking whether a calendar month is correct: it is a defined interval, and it either measures what you meant to measure or it does not.

If you want to describe the season a person was born into, the relationship between the Sun and the Earth's tilt, the tropical zodiac is the frame that tracks it, and it will keep tracking it for as long as the Earth has seasons.

If you want to describe where a planet sat against the visible stars, the sidereal zodiac is the frame that tracks that, and a telescope will agree with it.

Do they disagree about anything else?

A great deal, and the zodiac is the least of it. Vedic astrology uses whole sign houses almost universally, weights the Moon and the ascendant far above the Sun, works with 27 nakshatras rather than 12 signs alone, and has a timing system in the dashas that Western astrology has no direct equivalent for.

Those differences change a reading far more than the 24 degrees do.

What a chart cannot settle

Neither system provides evidence that the sky causes anything, and picking between them does not get you closer to that. What you are choosing is a frame of reference and a tradition of interpretation, and it is worth being clear that this is the choice on offer.