I have to agree with KoF on this one, and I'll expand on what he said to explain it better, I hope.
To dismiss his dominance as “running over small, slow white guys” is skimming the surface at best. The fact of the matter is he was a physical freak for any era of pro football. At 6-2, 232 lbs he was the same height and 10-15 lbs. heavier than Adrian Peterson. He practically dwarfs Marion Barber, who’s known as a human battering ram. Brown also had sprinter speed which stands up to today’s backs and possibly surpasses them. He did indeed run track in college (and played lacrosse, considered one of the very best to ever play that sport also). His 4.5 40 time seems a tad slow at first glance. When you see the truth of it though, you should realize it’s amazing:
Peterson ran the 40 in 4.4 while wearing shorts and a t-shirt and anyone who’s ever watched him (prior to this past weekend's knee injury) knows he has breakaway speed. What would JB have ran in a pair of shorts? I have to believe it would be better than a 4.4.
If you’ve seen clips of Brown then you know he ran hard as well. I know, all the defenders were small and slow. To some extent that’s true. As best I can tell without finding any hard evidence, the average linebacker was roughly 225-230 lbs and stood about 6-2 (a few sites allude to these numbers). Now, the average player at the same position is roughly the same height (maybe even a inch shorter) and goes about 20 lbs. bigger. Granted, they are probably faster as well. However, A 230 lb. freight train with great speed can still run plenty of players over and disappear if you let him turn the corner. By the way, Brown is bigger than Jonathan Vilma, London Fletcher, D’Qwell Jackson, Pat Angerer, and NaVorro Bowman to name a few. In fact, his playing size is within 10 lbs and 1 inch in height of most of the league’s top tacklers. That's not to mention that those small defenders of his time pretty much had carte blanche to try and decapitate ball carriers.
What's also overlooked is that he also played with much smaller, less athletic offensive lines too. Most people agree that the average player is bigger and more athletic than during Brown's time. This applies to lineman also. In 1965, Brown's final season, the average weight of the five regular starters on his o-line was 249 lbs. The heaviest guy was only 265. In today's NFL, he wouldn't have a lineman smaller than 300 lbs and most would be closer to 320. And just like the defenders they would be faster and operating in more complex blocking schemes. Therefore, it stands to reason that the blocking he got now would be at least as good as it was then. With that in mind, he'd probably still encounter first contact at about the same spot on the field he would be used to from his day.
I think Brown would be a beast in any era.