Speed.

Volley fire was about delivering the most ordnance possible as quickly as possible, to break the enemy's morale and rout them. British soldiers trained constantly to fire as quickly as possible. They also drilled in moving quickly into and out of formation, which was crucial to defend against certain types of attacks (particularly cavalry), and on how to quickly move from marching later into a firing line.

The British army was not particularly feared or well-thought of during the 18th century. The super-soldiers of the day were the Prussians which is why I imagine is one reason why the Americans were happy to have Baron von Steuban train the Continental Army.

In any case, jschootiger has answered part of it, but he didn't mention another important part: discipline. Discipline keeps soldiers in formation, following orders, and whatnot even when everyone around them is dying and a human naturally is going to want to flee. The Prussians were particularly famed for their discipline in battle and the brutal manner in which they forced it.

I was taught that the war was unpopular in the Isles so the government hired a number of German mercenaries to fight alongside the regulars. Is this true?

Soldiers in the British army had years of training prior to coming to America. Most of the American troops had no formal training and were farmers. This literally meant some American soldiers had only practiced marching for a few days prior to fighting on a battlefield.

The major difference between the two would have been discipline and understanding of battle tactics (orders). Soldiers which are not well trained / inexperienced will make mistakes on the battlefield. These mistakes can cost those soldiers and other soldiers their lives.

I'd answer that the Redcoats were feared by the population because they were a regular force and many of the Americans were irregular militia. It's natural that such troops will fear the regular army. War's a scary place. It seems clear from subsequent events that the Colonists got over their fear of the British.

The American Revolutionary War wasn't really the British Army's finest hour though. Back home indeed, soldiering was considered as something close to the male equivalent of prostitution: a job that any down-and-out could do if they couldn't amount to anything else. It's closer to the truth that the British Army in the ARW was fairly poor, and it was the lessons of that campaign that really galvanized the British into reforming their army into the force that would become a military terror in later years.