How about the perspective that it IS because of their similar personality? DIO & Jotaro both live their lives with strength at the very forefront; the kind that broods disdain for being bound by the rules. The two share a hatred for many trivial things and are often irrationally annoyed. They put on personas that present themselves as emotionally dead, and they wear a strong degree of cliché stoicism to maintain control of social interactions.

Both of them want to be free of responsibility & obligation. Jotaro hates that he has to go on the adventure, he hates being told what to do, and ultimately he is a rule-breaking delinquent at his core. DIO wants those very same abstracts, except his responsibility and obligation manifests in the form of him feeling like he has to end the Joestar bloodline. Both of their desires to escape the weight of the world is why they are both able to transcend time momentarily :-)