HTupolev

Depends on how much lighter, and what "significantly" means.
If the bike+rider system is 80kg, and you slash this by 2kg, that's a 2.5% reduction in gravitational drag. When you're moving slowly up a steep hill, this might actually give you close to a 2.5% improvement in climbing speed for the same effort.

"Stiffer" is more complex. As much as "stiffness" gets talked up, power transfer losses in rigid frames usually aren't all that significant, even with frames that by modern standards are considered very flexible. There's some evidence that differences in frame stiffness can result in tangible rider power output differences due to how their pedaling interacts with that flex, but this might not be quite as simple as stiffer=better.