In short, Fall of the Samurai is an excellent expansion that builds well on Shogun 2.
The focus of the new expansion is the rapid modernization of Japan in the context of Boshin War. Within the single-player campaign, you will see a transition from the samurai units from the original title to gun-carrying and artillery units of the early modern period. As you would imagine, this transition is a big one, but the game maintains the same fluidity of combat of Shogun 2. Unlike some other games in the Total War series, the gun and artillery units bring with them a tremendous and satisfying sense of power. I had a lot of fun in battles in this game.
One aspect of the Shogun 2 I did not like was the realm divide event that occurs at the end of the single player campaign. In Fall of the Samurai, this has effectively been replaced by an event where most or all clans form two Shogun- or Emperor-supporting alliances. I liked this event much more; the end game felt like it had a greater sense of focus, and being able to have allies throughout the campaign felt more natural and rewarding.
The expansion does not seem to have the same depth and balance of the original title. Clans are pre-divided into Shogun- and Emperor-supporting camps, so diplomacy feels a little canned. If you are pro-Shogun, you ally with other pro-Shogun clans. With gun and artillery units being as powerful as they are, your clan development is usually focused on researching and producing relatively few unit types. However, the game is so fun, it's easy to overlook this minor flaws.