As .500 says, it's largely an issue of prestige. Chopper lump tubes are usually used on more expensive guns. Mono-bloc construction doesn't get as much respect because so many cheap, low quality guns have been made that way.

In the days of damascus and twist steel barrels, lumps were usually dovetail (although there were a few damascus chopper lump guns built). As fluid steel displaced damascus, many of the very best British and European double guns continued to be dovetail lump, because that's what the older, experienced barrelmakers knew how to make. These were gradually displaced by chopper lump, and with respect to double rifles, also shoe lump.

Chopper lump is considered the best, but that's still primarily prestige. Steels that are truly ideal for barrels are not ideal for lumps and vice versa. The advantage of dovetail or shoe lump barrels (in other words, brazed on lumps) is that you don't have to use the same steel for both and no compromise is necessary. I don't know enough about monobloc construction to say, but the same may possibly be true of them. With chopper lump, the lumps are integral to the barrels.

In terms of real quality and durability, the barrel construction method isn't significant in comparison to overall built quality. Many fine double rifles have been made with all four methods and junk has been built with chopper lump barrels. My only gripe about monobloc construction is when the seamless method is not used. A visible join is unacceptable on a $10000 doublegun, whether shotgun or rifle.
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