The content of the large plates is that of the reigns and doings of the rulers. With these two verses, we can surmise a great deal about the content and transmission path of the two sets of plates. The large plates were the official record of the political kingdom. As such, they were the property of the throne (in whatever state it existed in Nephite politics, whether king of chief judge). The large plates record the doings of the kingdom, and would logically be passed from ruler to ruler.
The small plates of Nephi had a more narrow function, which was to describe the ministry of the Lord to the people of Nephi. In that context they would be free to leave out major political intrigue, and to concentrate on spiritual matters. We know the transmission path of the small plates of Nephi because we have them, and they were transmitted father to son, and at times brother to brother. This transmission path follows direct kin lines.
Where the kingship and the descendants of Nephi were one and the same, the transmission path of the large and small plates would have been the same. However, it is unclear whether or not many of Nephi's descendants ever sat on the political throne. It would appear that the two sets of plates separated early, with Nephi defining a separate purpose, and the separate provenance supplying even further differences as time went on.