The splitting of the fellowship allows for the plot and characters to get fleshed out more than the Fellowship.
We see the friendship deepen between Gimli and Legolas. Aragorn growing as a leader as he rekindles hope in Rohan. The other trio of Frodo, Sam and Gollum has some different pacing but brings out the differet strugglea they all face in trying to help in this increasingly impossible task.
Moving into Return of the King, we are left with a sense of hope and dispare. With Aragorn, Gimli and Legolas we get hope, through the saving of Rohan and a new ally, that Sauron may yet be stopped. Through Frodo, Sam and Gollum, we see them move closer to their goal, but further into despair as they experience growing evil and darkness.
As always, Tolkien's ability to describe an environment and land are incredible. Drawing you into Middle Earth and bringing it to life.