"Significant" defined how?
As for less weight .... How many minutes do you spend climbing on your favorite (or least favorite) climbs? How would you be willing to spend to save three seconds on a ten-minute climb? How many seconds on a ten-minute climb would you consider "significant"?
Pretty sure any losses due to frame flexibility are not significant except to the really anal nitpickers and the guys who still use slide rules. Biggest thing with stiffness with modern frames is when sprinters can actually warp the frame enough to have stuff rubbing ... but unless you are cranking out 1600 watts .....
And as far as carbon fiber .... CF is different, not better. A CF frame is not inherently better than any other. There are engineering reasons for using CF in certain applications ... but I ride an 17-lb CF wunderbike and a 27-pound Al working bike up the same hills at about the same speed. The engine is really all that matters.