the british empire may have been bigger, although i am not sure about that. but at the time of the british empire there were more people livining in more places around the world, so there was more land to conquer. the romans conquered almost all of the land that people inhabitted during that time.
mmmmmm
At about 1 AD the estimates of World population vary between 170 and 400 M.
In 1900 the estimates vary between 1.55 B and 1.762 B
http://www.census.gov/ipc/www/worldhis.html
I realise these dates are a little arbitrary but they’ll do for a moment.
A map of the Roman Empire at its greatest extent is here
http://www.acs.ucalgary.ca/~vandersp/Courses/maps/basicmap.html
and a similar map of the British Empire is here
http://www.britishempire.co.uk/maproom/maproom
According to this site
http://www.prb.org/Template.cfm?Section=PRB&template=/Content/ContentGroups/02_Articles/0ct-Dec02/How_Many_People_Have_Ever_Lived_on_Earth_.htm
the population controlled by the Roman Empire was between 45 and 90 M, out of a World population it estimates to be 300 M.
This suggests the Roman Empire had between 15 and 30% of the population, whereas the British Empire had between 470 and 570 M from a population of about 1.6 B, giving a percentage spread of 30 and 36%, suggesting the British Empire was slightly larger in percentage terms.
Due to the uncertainities involved in estimating populations, it would be difficult to prove which was the larger Empire in terms of the World population it controlled.
However, in terms of square km or square miles covered, at 36.6 M sq km, the British Empire was the largest the World has seen so far, followed by the Soviet Empire and a number of others, until the Roman Empire is reached at number 17 with 5.7 sq km.
http://www.hostkingdom.net/earthrul.html
Frankly, I consider a question like this to be similar to the type exhibited in the “what was the best gun of WW 2” in that it is subjective and cannot be resolved.
edit - to restore a link