The iPhone 6s is almost the same size as the iPhone 6—in inches it's the same height and width, but the 6s is bigger by fractions of a millimeter. The iPhone 6s is deeper, measuring 0.28 inches (7.1 millimeters). That’s 0.01 inches (0.2 mm) thicker than the iPhone 6. And the 6s weighs more, too.
There’s a good chance your iPhone 6 case can fit on the iPhone 6s. If you’re using a silicon or leather case, your case probably has stretched a little with age, so it may fit fine on a new iPhone 6s. Hard-shell cases are a different story—they’ll probably fit, unless the fit is already very tight on your iPhone 6.