carbon vs aluminium frame vibration absorption? bumpiness?
Aluminum has gotten a bit of a bad reputation from the early generation of frames which were overly stiff. This is less the case today as manufacturing technology fixed most of these earlier problems, and bicycle designers can create formed aluminum tubes that provide compliance (i.e., vibration absorption) in one direction (e.g., vertical compliance) and stiffness in another direction (e.g., lateral for power transfer).

Aluminum frames are actually an alloy (mixture of metals) and the there are a number of different alloy composition available, with each having different metalergic properties (e.g., stiffness or compliance, strength, etc). Frame manufacturers tend to choose an alloy that suits the intended use of the frame so they will often use a mix of alloys across their frame lineup. 

Tubing shape also has an impact on vibration dampening. Earlier generations of frames that were famous for being overly stiff used relatively straight tubing.  Modern frames often use hydro-formed tubes that have carefully crafted shapes to produce compliance in one direction and stiffness in another.

Essentially the compliance you feel in a modern aluminum frame was likely intended as a design feature by the manufacturer or the result design constrains such as cost.

Carbon is not a panacea for compliance either as the ride quality of carbon is directly related to the layup process (i.e., how layers of carbon fibre are compiled together with epoxy).  This is a very expensive and labour intensive process, where it is easy for manufacturers to cut corners in order to save money.  From the outside most (everyone?) cannot tell what, if any corners, were cut.   In the end the compliance of the frame is directly related to the manufacturing process, just as it is with aluminum. 

Similar to aluminum the compliance you feel in a modern carbon frame is the compliance intended as a design feature by the manufacturer or the result design constrains such as cost. You will have to ride the frame to see how it performs.

Now if we go back in time to the 80/90's both the carbon and aluminum frames, which both employed relatively straight tubing (earlier carbon frames had straight carbon tubes that were glued into metal lug joints), then yes as a general rule carbon was more compliant.  If we compare modern frames (of similar quality - key point) from the same manufacturer with the same intended use case (another key point) then the gap in compliance will likely be quite small.

GCN has a good video overviewing a lot of the points mentioned above.