Aragorn proves his leadership by accepting situations quickly and moving on, but Frodo does it too, only quietly and in his gentle hobbit way.
In the book Frodo puts up quite a fight before agreeing to take the Ring from the Shire; it is as if he knows when he takes it on he will not duck out. Gandalf has to be stern with him, but in the end Frodo does not obey; he acquiesces.
Also in the book Frodo lingers a long summer before leaving. He is not just reluctant, but wants to sever from his home. Even now, when the task is only to go as far as Bree, he intuitively knows he may never return and is saying goodbye. But as yet Frodo's resolve is fragile; when the Conspiracy is unmasked he is startled and angry; how could he have given so much away? It is the only time outside Mordor he turns on Sam, but Merry rescues the hurt and unhappy gardener by telling Frodo that he has given the game away by saying goodbye to every beloved place as they passed through it. Frodo will not be so open and unguarded again.
On Weathertop Frodo's resolve proves disastrously vulnerable and he puts on the Ring. He is wounded by a weapon of the dark.
At first in Rivendell Frodo thinks he will be released from his burden. He says it to Gandalf when he wakes up, and the Wizard looks sharply at him; he has reasons to think otherwise....
At the Council, like a neutral nation seeing itself drawn into a terrible conflict, Frodo realizes he can't put the Ring aside. It is as if he knows the darkness that wounded him has to be destroyed or will somehow destroy him eventually. The brave hobbit volunteer of the Shire becomes the centre of a whole war and a varied and courageous company of the great and the good swear to guard him.
But I would say it is not just the Ring they follow, Frodo inspires others to follow him. Even from the Shire three unwarlike followers cling to him. Boromir says 'You carry the fate of us all, little one' and in the book Aragorn quietly asks Frodo for 'permission' to be his companion again. The Quest is personalized in Frodo.
From Rivendell Frodo becomes much more inward-looking and quiet, careful, as if he knows that the fate of so many is on him. Really only Sam knows his mind and even then not completely. It is as if he has attained some state of enlightenment, but it is really a hard-won composure; watchful that he does not leave a chink for the Ring to slip through to dominate his mind. It is a heroic and unseen struggle, but by the time Frodo has reached Lórien Galadriel recognizes it and salutes Frodo as a Ringbearer in the true sense and not just a mule not understanding his task.
Galadriel answers Frodo's questions and the hobbit bows his head under knowledge hard to bear, but Frodo assimilates all Galadriel says, using it to strengthen himself, even though he is alone in bearing his burden and knows all along that attaining the goal must involve his own personal destruction.
By the time Faramir catches and interrogates two halflings Frodo is a tough nut to crack. But Faramir's trump card is his knowledge of Boromir's death, which Frodo is unaware of. When he plays it Frodo's desperate composure is shattered. He begs Faramir to let him go on his way as he has a task to complete 'before I too am slain' but the appeal which would melt a stone fails to move the usually compassionate Faramir, who loved Boromir his brother and is up to know how he died and will get it from this hobbit however he may.
Faramir never gets under Frodo's guard; in the end it is poor Sam who gives away the truth. Faramir, used to war and fighting, is horrified at Frodo's quest and the prospect of almost certain death. He tries to dissuade Frodo, who eventually has to literally hold over him the horror of a burned and blackened Gondor to convince Faramir to let him go. The hobbit has a resolve and tough-mindedness even beyond this prince of Gondor. Faramir salutes him and his awe and love for Frodo reflects the little hobbit's moral heroism.
As Aragorn fights battalions of orcs in the open field Frodo has as a battle ground his mind, from which there is no escape or rest.
Apologies, truly meant, to Frodo fans, only my own view of his journey.