I would assume this would be the same to some degree across all filter brewing methods.
This could depend on the brand of filters and the brewing method so it's worthwhile (and fun) to do the experiment. I'd love to see results from more experimenters.
Bamboo vs. Paper Filters: I did this experiment. We only had three tasters but the results were statistically significant at the 5% standard -- all three of us could taste the difference. The bamboo filter made sharper coffee (analogous to sharp cheese) while the paper filter made smoother coffee. We did not all have the same preference between those two batches.
Filtering out Diterpenes: According to the AeroPress FAQ question "DO YOU RECOMMEND USING A METAL FILTER IN THE AEROPRESS?":
We were originally planning to include a metal filter with each AeroPress but when we conducted blind taste tests comparing paper filtered AeroPress brewed coffee with metal filtered AeroPress brewed coffee, the paper filtered coffee always won.
We also learned using a paper filter is healthier because it removes diterpenes from coffee and diterpenes are potent agents that raise your bad cholesterol.
Q. Does anyone know if bamboo filters similarly remove the diterpenes from coffee? Are bamboo filters made from a combination of paper and bamboo fibers?