Most comparisons between Rome and the USA focus on American government and its geopolitical policies. I'm not going to rehash that as there a plenty of threads on it.
What interests me most is culture. Until recently the USA was presided over by a White, Anglo-Saxon English speaking Protestant majority. The language, culture laws and religions of the US are shaped largely by its status as a former British colony. Britain retained little of its Romanatis compared to the Continent after the Western Empire collapsed, internalizing the cultures of the Anglo-Saxon hordes, and thus this was passed on to America.
The WASP mentality has taken a hit in recent decades, thanks to the deconstruction of the academic counter-culture, as well as large number of non-WASPS entering the country.
Of the latter, the most significant are those from Central and South America, whom we call either Hispanics or Latinos. In contrast to WASP society, they speak a language descended from Latin. Most are Roman Catholic to some degree or another. They may and often do carry different cultural presumptions than Joe WASP.
Estimates project that Latinos shall form the majority of the American southwest by 2050 at the latest. They will form a significant presence in the urban areas of the rest of the country.
Clearly, every culture is potentially effected by a major demographic change. If a culture cannot assimilate an influx of "invaders" then it shall itself be assimilated. This particular demographic group is nearer and dearer to the Roman legacy than the current dwindling majority. Imagine a US that is officially bilingual with Spanish, where Catholicism is a much larger presence than now, and where Anglo-Saxon views on government and economy no longer predominate. In other words a US that is much more heavily influenced by the Roman legacy than it is now.
I find this all intriguing. And honestly amusing. The hand of Rome reaches out from the grave to conquer yet again.