One problem with this is the vast range of peoples that could be referred to as "steppe archers." The only specifics I was able to find about Eastern horse archer bows were estimates for bows used by Turkish horse archers in the First Crusade. Strickland and Hardy in The Great Warbow estimate that the composite bows used by such archers could range from around 60-100 lbs in draw weight, but this was not an absolute, as demonstrated by one usually powerful Persian bow of approximately 110 lbs draw weight. Compare that to the English bows recovered from the wreck of the Mary Rose (about the only real examples of longbows we have to work with), the majority of which had a draw weight of approximately 150-160 lbs. There are some outliers, of course, with the weakest bow's draw weight being 110 lbs and the strongest being an absurd 185 lbs. However, comparing draw weights is only somewhat helpful, as the design of the composite bow allows it to carry more energy for less effort. So the Englishman with a 110 lbs pound bow might have found that 110 lbs Persian bow to be pretty difficult, while a Turk with a 70 lbs bow might regard the freakishly huge 185 lbs Mary Rose bow to be the work of sorcerers. Ultimately, it depends on the individual archers involved.

Tactically speaking, the two sorts of units (English longbow archers and steppe horse archers) were used for very different purposes. English archers were often mounted (and could, in emergencies, actually shoot from their horses), but dismounted for any significant engagement and fought in large formations, defended by entrenchments and earthworks. Central Asian horse archers like the Turks or Mongols fought from horseback and loosed arrows both on the advance and the retreat. This is another reason for the use of the composite bow by these peoples: a smaller bow is better able to be used in a variety of positions within the confines of the saddle. They also typically used lighter arrows in order to achieve greater ranges than what might be typical of an English longbow, but using lighter arrows would come at the loss of penetrating/wounding ability.

In general, I find this kind of comparative discussion to be pretty useless. English archers in their heyday during the Hundred Years War simply did not encounter those sorts of groups, with the exception of English longbow mercenaries encountering Hungarian mounted archers in Italy in the 14th century. So unlike the question of, say, English longbowmen vs Genoese crossbowmen (for which there is a great deal of historical evidence to draw on for a comparative analysis), there is little we can say about the relative abilities of English archers vs steppe nomads that is of much historical value whatsoever. Dan Carlin is an entertainer, not a historian, and judging from previous statements he's made, seems prone to this sort of Deadliest Warrior line of thinking. There have been many previous discussions of Carlin's work on this sub, and I speak for quite a few of the flairs when I say that much of what Carlin says ought to be taken with a grain of salt the size of a steppe pony.