If Beau Brummel was prepotent to Don Carlos who was prepotent to Anxiety the 4th who was prepotent to Sir Thomas, then Beau Brummel would be a superior traited bull to all other linebred bulls including Anxiety the 4th and Anxiety the 4th should become obsolete in the herd because the best genetic combinations have already been selected for. That is, unless you made an incorrect selection of the bulls that were labeled prepotent. If I label a bull as prepotent to his HerefordSire to progress the linebred line, I am saying the bull is better than his HerefordSire. If the bull wasn't better than his HerefordSire, he wouldn't be labeled prepotent.
A bull becomes more prepotent because his genetic make up becomes more homozygous, for better or worse. Basically all you achieve is you limit the number of permutations in the random division of genes in the offspring, therefore the likelihood that the bull will stamp his influence on his get is increased.
If the selection was up to standard (and in this case it seemed to have been the case based on the success of the line) Don Carlos was obviously the halfsib selected to start the linebreeding process when mated to his halfsibs to concentrate the Anxiety 4th blood, these matings produced Beau Brummel who was likely superior to Don Carlos because of the concentrated Anxiety 4th blood (prepotency, what G&S wanted to achieve in the first place)
and because of the selection pressure towards their ideal animal.
When you look at the pedigrees you'll see Anxiety 4th is a linebred bull so we can assume he was more prepotent than Don Carlos, who was basically the result of an outcross mating. Beau Brummel would have been more prepotent than Don Carlos, but not neccesarily as prepotent as Anxiety 4th.
Clear as mud?