I think you are correct that, in the example you gave, distinctive is the preferred form. Here distinctive is an adjective that reflects a quality that can separate the object from others, and often communicates an implied "very".
His full body tattoos were distinctive.
Distinguishing is used more often as a verb form. While the participle distinguishing can connote that the object is capable of being differentiated from others, it seems less common and probably conveys a difference that is less than something which is distinctive.
There were distinguishing indicators in the various test results which allowed differential diagnosis.
Interestingly, the adjective distinguished, which derives from the verb distinguish almost always conveys a difference from other objects that is highly regarded.
I yield the floor to the distinguished gentleman from Kentucky. [Perhaps sarcastically.]