it it not yes/no stronger or not kinda answer a material can be strong or weak, but the end product strength and durability depends on the design and build and quality control.
as an example a quality carbon mountain bike will be engineered with lots of strength to take the stress of jumping and with enough material to deal with crashs etc, where a high end road racing bike will be engineered for strength where needed and less strength where not needed to keep it light. (often in the top tube)
There are reasons some manufacturers state don't use the top tube for clamping or transport
so in some cases the bike can fall over and you can damage it like in this thread
https://www.bikeforums.net/bicycle-m...bon-fiber.html
and in other cases you can crash a mountain bike with no problems
from what I have seen the chief issue with carbon is that when it fails, it fails fast without warning and it's overall structural integrity is as whole composite, so a deep cut into the composite can cause loss of integrity, so in general a lighter carbon bike should have more TLC and should be checked for potential deep cuts