We see this again in the Spanish prison, where it has serious consequences. Hornblower wants to study the situation: discover the number of guards, the times of their shift changes, and take the time to formulate a plan that will actually be successful. On the other hand, Hunter wants to take the first opportunity to attempt a jailbreak rather than wait for the best one, and he misreads Horatio's slower, deliberate approach to escape as a lack of will to actually do so. He convinces some of the other men to follow him in a futile attempt which ends disastrously.
Speaking of the not-so-great escape, part of the blame for this really does lie with Horatio I think, as it reflects a failure in his leadership. At the beginning of T.D.A.T.D., we see Hornblower at the top of his game, cleverly outsmarting his opponents and obtaining the first British victory in some time. As a result of this, his men are admiring and happy to follow him, convinced that he's smart and lucky. Then, when things go wrong, and Horatio is unable to keep them from being captured despite his best efforts, that confidence in his abilities is shaken. Hunter is able to sway the men despite his cockamamie plan because their incarceration is wearing on them and they desperately want to escape. This is where Horatio's habit of playing things close to the vest is less than helpful.