I think that the premises of your question may put the focus slightly off. The issue of Prussian VS Austrian hegemony in the unification process is very well documented in a lot of books (even any textbook) but was only one of the debates surrounding the question. The other major one was what kind of state and on which bases such a state would work once a unified Germany came to be and the pivotal moment of the debate is traditionally put on the meeting of the German conference in Frankfurt in 1848. This meeting was largely dominated by liberal moderates that initially had risen against the post-napoleonic order established in 1815. During 1848 all German monarchs were facing massive upheaval in their state and their reaction was largely the same: send in the troops. While the revolutionaries were crushed in bloody slaughter the moderate in Frankfurt faced massive problems in imposing any kind of power on the disunited states of Germany. The result was that by 1849 Austria, initially favoured, did not want to compromise on her hegemony and the delegates turned to the King of Prussia, Friedrich Wilhelm IV, as a potentially more confederation-oriented monarch than the Austrian Emperor. However, the King refused the offer because it would bind him to a constitution that he had no significant part in planning. Therefore, the project effectively collapsed until Prussia did not effectively managed the unification fairly autonomously.

Bismarck, as the other comment has already underlined, was at the start of his career a conservative man with the support of a significantly conservative class and therefore was part of the supporters of the refusal of the crown offered by the Assembly in Frankfurt.

It is important to understand German unification in the historical context of the geopolitics of that historical period and preceding historical periods. This geopolitics was defined by the threat posed to Prussia and other small German fiefdoms by the great powers; this threat resulted in the Prussian strategy of annexing surrounding territories to bolster its strength and support its self-preservation.

There's the broader context of territorial aggression in the Great Powers milieu which dominated European geopolitics in Bismarck's lifetime, and for many centuries before and after. In Western Europe this ended after the horrors of the Second World War, and the borders of Western & Central Europe have been fixed since 1945. Territorial aggression continues today in Eastern Europe.

In Bismarck's early life, there was no unified German nation-state. The various German fiefdoms were incredibly small compared to the centralized nation-states –  each German fiefdom was only a tiny fraction of the size of a centralized nation like France or England or Russia. The German fiefdoms – having smaller populations and smaller economies – could only field a much smaller military force that was inevitably far weaker than those of the centralized nation-states.

The essential and fundamental concern of the tussles between nation states was acquisition of new territory and defense of existing territory. Borders were continually shifting.

In this context, every German fiefdom (and its monarch or leader) had as its primary concern its very existence – geographically, Germany was surrounded by great powers, France to West, Russia to East. And the desire of these great powers was to annex the territory of the smaller German fiefdoms.

For this reason, Prussian society was massively militarized, allowing it to field a military force far greater than its economy and population would typically allow – though its military was still far smaller than a great power military. Prussia used its military to expand its territory to increase its ability to defend itself against the Great Powers.

​

references:

Paul Kennedy. Rise and Fall of the Great Powers

Hagen Schulze. Kleine Deutsche Geschichte.