Cannon or chariot — which is better?
These answers restate the rules implemented by our open-source engine, which follows the WXF laws for movement, checkmate and both repetition rulings: a side that forces a repetition by perpetual check or perpetual chase loses rather than drawing. The chase half has not been validated against the official casebook. Where an answer refers to a specific position, that position lives on the linked reference page, where the build verifies it before publishing.
Direct answer
The chariot, and it is not close: about 9 against 4.5. The chariot captures whatever it reaches along an open line with no conditions attached, while the cannon needs exactly one screen and therefore spends much of the game unable to capture the thing it appears to be attacking.
Why the gap is so large
Reliability. A chariot's threat is a threat now and will still be one next move. A cannon's threat depends on a piece it does not control, which either side can move. When you count attackers around a palace, a chariot counts as one attacker and a cannon counts as "one attacker if the screen stays".
When a cannon is worth more than usual
Against an intact defence. A palace full of advisors and elephants is full of screens, so a cannon attacking into it retains all of its value — which is exactly the situation where a chariot alone cannot break through. Two advisors and two elephants normally hold a lone chariot to a draw.
Related questions
Should I trade my cannon for their chariot?
Yes, essentially always. It is winning about four and a half points of material.
Is two cannons better than one chariot?
On paper roughly equal. In practice the chariot is usually better, because two pieces need time to coordinate.
.