The British and American leaders during the Revolutionary War faced different sets of challenges that made for a difficult war to fight. British challenges often centered around the fact that they were fighting the war overseas, while American challenges often dealt with the fact that they were an upstart new nation without the resources and professionalism of the British.
For the British, fighting a war overseas in the eighteenth century was not an easy task. Major decisions or requests that needed to be proposed to the British government for approval would require great amounts of time as the information traveled over the Atlantic Ocean by boat in an era before the telegraph. Leadership in the British government in London were basically fighting the war, and receiving updates, on a weeks long delay. This led to issues in terms of supplies and reinforcement, as requests for such often took significant time to be approved, gathered, and shipped to the Americas.
Additionally, the British were fighting the war in territory that they were not as familiar with. They would be required to rely on information from colonial loyalists and Native American allies when they were available. This gave an advantage to the Americans who lived on the land and had a better knowledge of its terrain.
Also the objective for the British to win the war was also more difficult. The British had to force the colonists to stop their fight for Revolution. This meant that as long as some of the colonists persisted, the war would continue. What makes this even more difficult is how invested in independence many of the American leaders and soldiers were. The British, on the other hand, did not have the same level of emotional investment.
Finally, the British were forced to fight a force that would not always meet them head-to-head on the battlefield, as was typical for European armies at the time. While the British had a very well-trained and professional army, they were trained in the line infantry style and tactics used in Europe. They were not as well prepared for the guerrilla warfare tactics that would be used against them by the Americans.
One of the biggest challenges faced by American leadership was their lack of funding and military strength. Being that they were part of the British Empire, and that they were in rebellion, means that they did not have easy access to military supplies which were still in control of the British. Cannons, ships, and other necessities were not as readily available, especially at the start of the war. The British, however, had a vast amount of wealth to draw from for their war effort. The United States would eventually procure the assistance of France and Spain to help with these issues.
American leadership also faced the challenge of having few well-trained soldiers. One of the reasons for the adoption of guerrilla warfare tactics was the fact that their poorly trained soldiers did not perform well in head-to-head line infantry battles against the British Redcoats. Baron von Steuben, a former Prussian military commander, would come to the United States and provide significant training for the American forces. Von Steuben focused on establishing discipline and drilling proper tactics into the American soldiers. This provided them with greater ability in the field as the war went on.
American leadership also faced challenges in keeping their soldiers from deserting. In the winter of 1777-1778, the American forces made camp at Valley Forge in Pennsylvania for the winter. It turned out to be a particularly harsh and cold winter, only made worse as food supplies dwindled and disease rampaged. The great challenge for George Washington, the commander at Valley Forge, was keeping his men from giving up the difficult conditions and going home.
Finally, American leaders also faced the issue that not all of those in the colonies supported Revolution. While most Americans supported the cause, there was still a significant number of loyalists who supported, and provided assistance to, the British.