It would depend on the army, but Richard was not the 'best' (although defining what constitutes the 'best' is difficult) knight in England.

The most famous and the 'best' knight of his age was undoubtedly William Marshal. When Richard was rebelling against his father Henry II (1189) the Marshal was involved in a battle with Richard. He, famously and purposefully, killed Richard's horse instead of harming Richard. That said, the Marshal was supposedly the only person to ever unhorse Richard.

Richard was a fantastic and renowned warrior among his contemporaries. He earned his nickname (Coeur de Lion) suppressing the Aquitaine barons who had joined the rebellion against Henry II of 1173-4, won the respect of Saladin and the fear of the Muslim population of the Levant and Egypt.

It is difficult to dissemble from chronicle sources what was praise lavished on a monarch, prince, or duke and what was a genuine reflection of Richard's abilities, but I do not think the sources are too far from the truth. Even his ecclesiastical critics, such as Ralph of Coggeshall, admitted he was a military hero, if a cruel one.

Richard was entrusted with difficult martial endeavours by his father, was well respected and loved by his soldiers and knights, he fought numerous campaigns both in Europe and the Levant, and demonstrated remarkable nous both in constructing and dismantling castles across France. He proved time and again his capabilities as a commander, warrior, and ruler.

For an excellent biography see:

John Gillingham, Richard I, (New Haven, 1999).

For a collection of excellent essays and a monograph by the same author see:

Richard Coeur de Lion: Kingship, Chivalry and War in the Twelfth Century, (Oxford, 1994).

For a contextual overview of English history in this period see:

David Carpenter, The Struggle for Mastery: Britain 1066-1284, (London, 2004).