Contrast valuing with the zero-coupon yield curve and valuing with an arbitrage-free binomial lattice

For an option-free bond, pricing with the zero-coupon curve and pricing on a calibrated binomial lattice give the same value, because the lattice was built to reproduce that curve and fixed cash flows do not depend on which path rates take. The lattice earns its extra effort when cash flows do depend on the path, as with callable, putable or capped instruments, since it shows the rate at which an option would be exercised in each state. Volatility then affects value. It is tempting to expect the lattice to give a different value for a plain bond, perhaps because it includes volatility, but it should not unless it is mis-calibrated.