I know that the Civil War armies were said to make a miserable show to Europeans, but how did the Continental Army perform by European standards?

Great question!

The answer to this will depend firstly on when in the way you're asking about, and secondly on what scale you grade an army's capabilities on.

At the start of the war, the Continental Army was, by almost every standard, terrible. The army that amassed outside Boston and later fought around New York City had poor officers, little discipline, uncertain supplies, and a patchwork of enlistment contracts that made its size unpredictable at best and doomed to extinction at worst. While the army won at Bunker Hill, that was more a testament to Gage making the wrong decision (a frontal assault), then lacking the manpower to launch a flank attack. Around New York, the Continentals were repeatedly outfought bad outmaneuvered by the British and Hessian armies, even in the wooded and broken terrain that was supposed to favor American troops. In one of the war's most catastrophic defeats, poor command and control of the army led to a force of 3,000 Americans staying in Fort Washington well after the position should have been abandoned. A Hessian assault force captured this garrison, and and an even more valuable cache of supplies, in one afternoon with minimal casualties.

Even in the early years of the war, the Continental Army showed signs of promise. Knox's transport of 200 cannon from Fort Ticonderoga to Boston during the winter of 75-76 was a master stroke that effectively created the army's artillery branch in one go. Patriot troops captured Montreal and nearly seized Quebec in a daring and difficult winter campaign. Individual units fought well during the New York campaign, and American troops consistently demonstrated the ability to rapidly build large fieldworks. Washington's winter campaign in 76-77 saw a hardened core of veteran survivors of the Battles of New York surprise and out-maneuver well-commanded British forces in Southern New Jersey, doing permanent harm to the British war effort by making them look unable to hold territory the conquered or to defend the loyalists who publicly opposed the rebellion. Continentals stalled and swarmed a British attack towards Albany in the Battles of Saratoga, while Americans managed to make fighting retreat d at the Brandywine and Germantown I that fall of 77.

Between 1778 and the end of the war in 1783, the Continental army got more technically proficient as it professionalized. The Continentals fought the best units of the British Army to a draw on the open field at Monmouth, made successful night attacks at Stoney Point and Yorktown's Redoubt #10, and demonstrated incredible resiliency in the "fight, get beat, get up and fight again" chase across the Carolinians. At Yorktown, the Americans laid an exceptionally smooth formal, conventional siege, arguably the defining trait of military craft in the 18th century.

Why, then, do I still have reservations about calling the Continental Army good? First and foremost, their performance was inconsistent. Gates bungled the Battle of Camden in catastrophic fashion. While Morgan and Greene did led Cornwallis on an epic chased across the Carolinians, they could not stop him from invading Virginia, freeing thousands of slaves, and nearly capturing Thomas Jefferson as he fled off his plantation.

Most importantly, the Continental Army grew increasingly mutinous in the latter half of the war. Between 1780 and 1783, the Pennsylvania Line mutinied twice abs the New Jersey line once in situations that stretched for days and resulted in some loss of life. Connecticut troops rioted in their camps at Morristown and West Point. The officers of the army gave some support to a plan by one of Gates' aides to march on Congress if they weren't guaranteed pensions.

In short, if I were drafting an army for a fantasy league of 18th century empires, I would not take the Continental Army. Their greatest victories involved either surviving defeat or substantial French assistance. They frequently seethed with discontent, as mutiny never seemed far away for both Continental soldiers and their officers.

Sources

Martin and Lender, A Respectable Army

Fischer, Washington's Crossing

Niemeyer, America Goes to War