That will depend on what happens in future of course, but it is doubtful if the US could ever be seen as equivalent to the Roman or British Empires. Those were physical empires that lasted for centuries, and during their time they were undisputed masters of vast areas of the world and they were never seriously challenged militarily.
In contrast the US has only even been a world player for bit over 100 years. It has been a military and cultural power since WWI at best. Until WWII it was seriously challenged by both Germany and England militarily and numerous nations culturally. Since WWI it was seriously militarily challenged by the USSR until just 20 years ago. During a lot of that time it was surpassed by the USSR in terms of technology and military might and at any time during that period its enemies could have utterly destroyed it within hours. Culturally, the US has had a lot of influence since WWII, but the US has also *absorbed *a lot of other culture. With the other superpowers gone, the US has demonstrated no real might or influence, as the debacles in Korea and Iraq are demonstrating. And it seems highly likely that China, India and the EU will seriously challenge the US within the next 20 years.
Historically the US is in no way comparable to the British or Roman Empires. It is a very, very brief blip on the world stage, and even when it does appear it is only one of many superpowers for most of that time. If things continue the way they are then the US will only have been vaguely comparable to those empires for a few decades.
Really, the US is just a footnote to the chapter on the “Industrial Period”. It is not a major, prolonged player of our time period. For a scholar of the distant future, studying this “Industrial Period” as a scholar of today might study the Middle Ages, the US will scarcely rate a mention except as one of the numerous powers involved in the prolonged 20th century conflicts. The activities of Britain, Spain, France, China, Japan, Russia and the German states, in contrast, last for centuries and have major historical ramifications, including the very creation of the US.
It seems likely that it will be remembered, at best, as something like the Hittite empire, though even the Hittites managed a few centuries as a superpower. Perhaps a better comparison would be to the Vandals. A group that was ascendant for a few generations, a group that had significant impacts on the established cultures of the world, but whose influence faded rapidly and has been relegated to a footnote based on their effects on the Roman, Greek and Egyptian cultures. I suspect the US will be treated the same way. A brief flowering of a rebellious branch of the British empire that had an effect on the machinations of the Important Cultures at a turbulent time in history. IOW remembered for the influence it had on other, well-remembred, cultures.