The reference to the ambassador in the singular suggests there could be multiple comparisons being made here. Firstly, between an ambassador and a leader, or their government, and secondly, between an ambassador and a private citizen.

The comparison is focused on the sanctity of the ambassador's position, meaning that Washington sees the private citizen, the leader, or the government, as lacking the same sacred value.

My interpretation of this would be that an ambassador is historically a protected class: ambassadors arose from envoys, and have enjoyed diplomatic protections from the countries they reside within.

Conversely, a private citizen, who may have hired spies in Washington's time, was not protected in the same way from their competitors. Taking action against an ambassador would be a serious crime.

On a larger scale, actions against governments are somewhat protected because of the diplomatic ramifications, but spy-craft is an ancient practice that has never gone out of fashion.

Spies can be used to protect the interests of their masters, to forewarn them of attacks, to be the canary in the mine so to speak. Ambassadors would have no need of this, or at least the appearance of no need, due to their protected position.

The other aspect would be the offensive use of spies in intelligence gathering and the like. In this respect, an ambassador has much more capability of gathering information about a rival than the private individual or the government. Ambassadors 'sacred character' as Washington calls it gives them position within a foreign country, as well as contact with members of the government, and many opportunities to network. They are, in short, trusted persons. Somewhat ironically, this is one of the reasons why embassies and intelligence communities have a lot of cross-over: spies piggy back on the diplomatic protections which are offered there, as seen during the Cold War with Russian and American spies being stationed as attaches in embassies.

So, to recap, an ambassador's 'character is sacred' is referring to the privileged position an ambassador holds, and the unparalleled access and protection this gives them. This privilege eliminates the need for spies, as they can gather intelligence themselves, and are often protected by both their government and their host.

I could also be wrong on all of this, but I hope if I am, I'll be corrected.

EDIT: Reading the original story from Washington's writings it seems the enemy sent some men forward to reconnoitre the territory Washington was in, and when he captured them they claimed to be ambassadors. Their orders and actions contradicted this, and Washington's quote was in defence of his decision to take them prisoner, which if they had been envoys, would have violated the traditional protections of an ambassador. But, as he points out, they had a 'slulking-place' and came close to his camp, yet never approached to deliver a message, which is the purpose of an envoy.

Hopefully the link + the edit text + the background on envoys will be enough to answer this!