Yeah, the similarities in the epic theatre structure are quite strong - have a look on Youtube at the discussion at the class discussion with the director.
There is religion similarity.
There is obviously black vs white similarity.
There is naming of the land that the grandfather says.
One difference might be with the overlords. In the LM, the plantation owners, including Whitechapel knowingly manipulate their 'christian' beliefs so to align it with slavery. In BD's even though Ernie had his skin 'painted on' when he returned, even though Bertie was left a derelict, even though most were not accepted when they returned, this was due to local acts of racism and bureaucratic exclusion that was racist but was not done for profit. The aborigines were dehumanised, called a 'calf' etc, but it was more xenophobic than the cruel use of another for profit as in slavery? Thje profit motive adds an extra dimension.
Another difference, quite obvious too was that in BD's the violence was perpetrated against men, totally exclusively. You could say that both societies existed in a time of war, but in the WW1, the black diggers found acceptance by their countrymen. In the war between the races in the south of America, there was no acceptance. Although Whitechapel was tolerated, the text starts off remembering and inferring that he recognised he had made a mistake in his previous mindset of being a good slave to survive. The similarity in both texts that racism is based on superficialities - in BD the soldiers could fight as well as any other, in fact braver as in Tommy and Mick - and in LM, Whitechapel was killed by his white half brother, which would have been murder if Whitechapel ahd been born white - but the difference is that the racism in BD is much less recognised as racism by the overlords. Nigel has to find solace in a mental institution, Ern has to give his medals away, Tommy becomes a vagrant - the letters all say similar, and as Archie finds, no one wants an 'uppity' black. The arguments put by Lydia and perhaps Whitechapel were clear and foreshadowed the end of slavery.
So, it may well be that LM is a more optimistic text in that the slavery did end and the longest memory survives. The kind of apologist thinking of Whitechapel is seen for what it is, and even though he is heroic, he was mistaken in his belief that slavery will last forever. In the BD, there is little reconciliation of those who went despite speaking teh same language, following the same religion.