Adapted from a couple of previous answers:

Byng's execution had a profound effect on the Navy of the mid-1700s. For one thing, it taught admirals (and other officers) that no matter how good their political friends, they could not escape the consequences of failing to act, and could not be perceived to be shy of offering battle. If there were plenty of things that could go wrong when attacking the enemy, on the other hand it would be a fatal error not to attack. The culture of determination in the face of adversity that the British navy cultivated over time certainly owes something to the example of Byng, though how much it owes to that is hard to quantify; it was reinforced throughout the decades by continued success in the face of even superior forces. Over time, the British assumed that they would attack whenever they saw the enemy, while the French and Spanish (and other foreign fleets) expected to be attacked and more than half expected to lose.

A bit of an additional question; were British fleet commanders and captains more aggressive and 'daring' than their French and Spanish counterparts in the Revolutionary and Napoleonic wars?

Yes, I think that they probably were, for three reasons:

• Their fighting instructions mandated extreme exertion to "take, sink, burn or destroy" enemy ships without regard to the cost to their own safety, with some caveats about hazarding the fleet for little reward. In the Battle of Minorca (1756) British admiral John Byng and his captains were extremely cautious in engaging the French fleet, regardless of the fact that they had been ordered to break through it to relieve the British garrison at Minorca (a strategic point in the Mediterranean). After the battle ended inconclusively, with light damage to the British fleet, the captains held a council of war and voted to retreat to Gibraltar.

The desultory battle and the fall of Minorca was a national scandal; the Admiralty court-martialed Byng and shot him on his own quarterdeck. (This is the origin of Voltaire's quip in Candide, Dans ce pays-ci, il est bon de tuer de temps en temps un amiral pour encourager les autres -- "in this country, it is wise to shoot an admiral from time to time, to encourage the others."). Jokes aside, captains were expressly rewarded for being aggressive, even to the point where disobeying orders was ignored or sanctioned if that resulted in the capture or destruction of enemy ships.

• The admiralty offered prize money to captains who captured ships, as well as head-money for prisoners and some other forms of compensation for service. Captains were entitled to three-eighths of the total value of a prize, unless the captains were under a local admiral's orders, in which case he was entitled to a third of the captain's share (one-eighth the total value). This lead to some unseemly chasing after prizes, but it rewarded capturing enemy commerce as well as enemy men-of-war.

• Most importantly, the doctrine of the British navy focused on destroying the enemy's fleet as the ultimate goal of naval warfare. Convoy duty, transport duty and even commerce-raiding were subordinate to this, and seen as dull but necessary parts of the business; even blockade duty was monotonous to the extreme but held the possibility of a decisive fleet action at some point. In contrast, the French and Spanish fleets were seen as an auxiliary or subordinate arm of their larger military, and their ships were more often thought of as basically escorts to move troops around.