They're a bit thinner than the original 335. I measured 4 centimeters, that would be 1.57 inches. That's 3 millimeters or 0.118 inches thinner.
Other significant differences would be the rim which is not laminate but solid maple in the case of the Heritage and the position markers are real mother of pearl instead of Gibson's plastic. I've tried a Gibson 335 and I noticed hardly any differences in playability. Haven't tried the Gibby in real life situations, but I trust it will be fine. The Heritage is superb - at least mine is.