Totally, acid functionalization of carbon-based materials may not have a very desirable results unless the functrionalization is conducted followed by other chemical process to induce more functions onto the substrate. The processes like grafting or polymer wrapping may work better that just acid-functionalization.
It depends on the defectiveness of initial material. Usually, CNFs are more defective and oxidation of them is more intensive. But "CNF" is a broad concept as well as CNT because CNTs may have highly defective "fish-bone" structure or ideal cylindrical structure which is very hard to oxidize.
It would be difficult to say which is easier to be oxidized in acid treatments, especially refluxing in strongly oxidative acids. Theoretically, CNTs should be more susceptible due to the existance of carbon ring curvature and pentagon carbon rings. While ideal CNFs are pure sp2 hybridized carbon chains containing termination groups at both ends. However, actual results may differ significantly. For example, if a large amount of defects and dangling bonds were found, such sites would be easily attacked by acids. Therefore, final results depend strongly on the products you obtained.
Obviously it is CNT. Generally, the number of layers in CNT are fewer than in CNF (generally in hundreds). Acid oxidation is more susceptible than CNF. It was my personal experience too.