The situation is very complex and hard to answer almost 1000 years after the fact. I would recommend that you read Asbrige's book „The Crusades“. While it deals with the crusades in their entirety, the 3rd Crusade is given great attention.

To paraphrase, Richard was undoubtedly a brilliant tactician. Several of his victories tell that he acted decisively in battle (during the battle of Java he seized the moment and pulled off an amphibious assault on the city just hours after Saladin's forces had all but conquered it), with great physical courage (It is reasonable to have doubts about many Medieval tales, or some of their more dramatic aspects, but the stories about the Lion Heart leading his soldiers into battle are too many to discount, e.g. during the contest for Jaffa), kept good discipline (e.g. during his march along the coast in the Holy Land his army always kept battle formation), didn't fall for simple ruses (fake horse archer retreat) and understood logistics (e.g. during his march along the coast he resupplied via ships, also, he ultimately decided against attacking Jerusalem, in part because he assumed that the siege camp could not be supplied [altough it must be said that this decision in particular came from a number of factors]).

But you asked about strategy, not about tactics. The reason I first answered about tactics is, because many people do not know the difference. Also, the answer is more difficult still. Richard is often seen as rash or reckless (“Warrior king”), and sometimes this is true. The most famous example is of course when he slighted the duke of Austria. However, he could also be very rational. E.g. when he decided against attacking Jerusalem, he advocated for attacking Egypt instead. As Saladin was at Jerusalem, the crusaders could have taken out his powerbase, which would have discredited him as a ruler, potentially inviting his vassals to abandon him. Bear in mind that this is ultimately just speculation (Several later crusades were destroyed trying to take Egypt), but it does not change that it was a sound strategy. Richard's men, however, wanted to attack Jerusalem (the goal of their crusading quest), without being detoured to Egypt. Richard, in turn, failed to understand both his men and the nature and limitations of crusading warfare. But on the other hand, he might just have understood these exceedingly well, because taking Jerusalem would have immediately ended the 3rd Crusade, as the bulk of the armies would have left (this is what happened after the 1st Crusade), leaving Saladin to reconquer it a few years later. Ultimately, the resulting indecision delayed the Crusade until Richard had to go back to England to sort out his brother. So what does all this say about Richard as a strategist? Well, easy: I do not dare to answer. Especially, as Richard was not exclusively a General, but also King, a Knight, and a Crusader, all at the same time (inspiration for this line goes to Asbridge, you really should read his book).

Saladin was a very effective statesman and strategist. He started with next to nothing when he arrived in Egypt and, based on his own merit, worked his way up to become the most powerful Muslim ruler in the Levant. In this case, the results speak very loudly in his favor. However, he also did leave Tyre undefeated after taking the rest of the Kingdom of Jerusalem, leaving the Crusaders a vital foothold in the Levant within reasonable distance of Jerusalem. He also failed to break the siege of Acre, which would serve as a magnet to Crusaders until the proper Crusade arrived and took the city. On the other hand: Hindsight is 20/20, and Tyre was an island fortress, making it next to impregnable.

It must also be said that Saladin's “endgame” might not live up to his earlier successes. Saladin funded his rule with assets he conquered by military means and his right-to-rule was based on his promise to conquer Jerusalem. Without spoils of war and without a “holy” cause it stands to reason that Saladin's peacetime successes might not have been on par with his military successes. This already became apparent during the time between his conquest of Jerusalem and the arrival of the 3rd Crusade. E.g. Asbridge notes that another reason why he did not take Tyre was that he just could not afford the necessary army for the necessary amount of time, turning to easier pickings instead. We will, never know, however, whether his rule would have stood the test of time, because he died shortly after the 3rd Crusade and the empire he had built immediately fell apart in dynastic disputes.