Here's the deal: this cycle is called The Lord of the Rings, and Frodo is our Ring-bearer. If his quest fails, all of Middle-earth will be destroyed. We'll just leave it at that.
While Frodo is the main character of Book Four (arguably the more important of the two books, though we like both), Aragorn's quest takes center stage in Book Three. Aragorn is developing his skills as a leader in this book, as he guides Gimli and Legolas in pursuit of the orcs who took Merry and Pippin. Once Gandalf reappears and then disappears again to go and meet with the Ents of Fangorn, it's up to Aragorn to support Théoden in the siege of Helm's Deep against the orcs of Isengard. Plus, Aragorn is developing new bonds with the leaders of Rohan that will serve him well when he needs men to help defend Gondor against Sauron.
One of the best indicators of Aragorn's growing power and importance in the narrative of The Lord of the Rings is the fact that Éowyn, who is otherwise a pretty cool customer, falls in love with him at first sight. Aragorn is really developing as a character in Book Three, and Éowyn's regard reminds the reader that Aragorn is a character to watch out for in The Return of the King.
Gandalf does not take center stage in the same way that Frodo and Aragorn do. But he is clearly a major figure in all of their plots. First of all, everyone recognizes him, from the elves to the dwarves to the men of Gondor to the Ents. Gandalf has been around for a long time making connections with all the good folk of Middle-earth. What is more, without Gandalf's sudden return, the two plot lines of Aragorn looking for Merry and Pippin and the Ents rising against Isengard would never have come together.
It is Gandalf who breaks Saruman's spell on Théoden, and it is Gandalf who appears at the siege of Helm's Deep on the back of Shadowfax, backed by 10,000 Huorns. Of all the characters in The Two Towers, Gandalf is the one who is most in the know about what is going on across Middle-earth. He is the one who weaves the different narrative strands into one recognizable picture.