By 1904 the lowest graded hammer gun made F grade was available with three barrel options, cheapest was Royal Steel, which was a fluid steel barrel, next was Best English Stub Twist, and finally Good Damascus.
If I had my choice of the two and condition was the same on both, I would choose the Good Damascus.
You are very fortunate to have these two guns without honed barrels.
According to Greener, by 1903 all damascus production had ceased in England. So you most likely looking at Belgian imports.
The reason Twist was cheaper, was that it took less man power to construct the billets at the rolling mills.
Pete