- X lived for m years and fathered Y
- X lived n years after fathering Y and fathered sons and daughters.
- All the years of X's life were m+n years, and he died.
The obvious difference between the two may be the fact that the ten generations until נח ends with the destruction of the world in the מבול. The ten generations from נח to אברהם ends with the reestablishment of belief in Hashem and the beginning of what will become the Jewish people.
This is discussed in a number of places. Rabbi Munk references רבינו בחיי. It is also discussed in ספורנו and כלי יקר and אור החיים as well as Rabbi Zalman Sorotzkin's אזנים לתורה (Insights in the Torah). The difference is connected to the the fact that the ten generations from אדם to נח lead to the end of the world and the מבול. On the other hand, the ten generations from נח to אברהם leads to the birth of אברהם אבינו. Rabbi Munk points out that this is the beginning of the development of the world that will end with the coming of the משיח.
Rabbi Sorotzkin says that the extra פסוק is to point out that this is actually a praise of the people who are listed as it emphasizes that they died natural deaths and were not punished by being killed in the flood. This is similar to the explanation given when בנות צלפחד explain that their father "died in the desert" in order to show that he was not part of those who died because of the rebellion of Korach or one of the other explicit punishments for the various sins. As רבינו נחיי says, there is no need for the third pasuk since the flood was over and we would no longer need to emphasize the fact of "natural" death.
An alternate answer given by Rabbi Sorotzkin (and others) compares the deaths in the מבול to the death of יואב. The גמרא states the the extra phrase "he died" means that he did not leave any children. The מבול can be considered the complete destruction of the world, and נח, far from being an "heir" of his ancestors. can be considered a "new creation". Thus, everything that happened before has been wiped out and is "dead".
The first death explicitly given in the genealogical table between נח and אברהם was פלג (Peleg) who died in 1996, the year of the dispersion. At that time אברהם was 48 years old. Thus all of his ancestors were alive, not only at his birth, but for the significant occurrence that ended that stage of existence. The Medrash says that Avrohom's brother הרן was the first person to die while his father was still alive, and by implication, he would have been the first person to die since the flood. As a result, the medrash of the כבשן האש had to have occurred while נמרוד still controlled the "civilized" world before the dispersion. This means the the actual major event of the age, the refusal of אברהם to succumb to the idolatry of his age and the initial revolt that led to מתן תורה and will lead to ימות המשיח, occurred while every link in the generational chain was still alive.
The final end of the generations also shows the difference between נח and אברהם. אברהם tried his best to save the world, and whether he succeeded or not, as with his brother or with סדום, the attempt still allowed the world to continue and led to life. The names show the difference between them. נח basically sat back, did what Hashem told him and left it at that. While he was saved, the entire world died and it was as if he was a new creation starting from scratch. אברהם worked and strove and not only became the "father" of the future, but was able to keep his ancestors alive as well.