According to one study, they are a lot a like. This has definitely been my experience.
Here is a taste of Zaid Jilani’s piece at Quillette:
Until now, the personality linkages between authoritarian right-wing and authoritarian left-wing individuals was based largely on informally pooled anecdotal observations. This is perhaps the first time that the personality congruence between these two emerging groups—nominally progressive Politically Correct Authoritarians, and alt-right White Identitarians—has been studied systematically. And the results reinforce the social sense that many of us get from our most ideologically intolerant co-workers and social-media contacts: Notwithstanding their diametrically opposed political postures, both hard Left and hard Right seem disproportionately populated by individuals who are impelled to control others’ behavior, and draw attention to themselves.
Read the entire piece here.