All true, but the set piece battles did not determine the outcome of the war, which is where the European comparison breaks down. In a traditional European war of that time you would have several major battles and then one side would probably start grumbling about peace. Then you’d capture a few major strategic points and the peace talks would get more serious, and the war might even end at that point. One side wins a few more big battles and captures a few more places of strategic interest and then typically the losing side would sue for peace and they’d work out some deal where the victor got some portion of what he already held. That was typically how it happened because the victor at this point was happy to keep a few provinces and give a few back to the defeated party in exchange for not having to fight for several more years to totally defeat the other party. Plus, when we’re talking about major power conflicts the real prospect of a total defeat was not high, and all the European great powers were extremely protective of the balance of power and would not allow another great power to lose so decisively as to upend that power structure.
In the colonies the British had three serious problems. Because of the position of King George in reference to the aims of the war, the British had to fight for much harder objectives than would have been typical of a European conflict in this time period. Namely, since the King saw the colonies as British provinces in insurrection he was not willing to sue for peace or parley some negotiated settlement, instead he demanded absolute conquest and submission.
The second serious problem was the colonies had extremely decentralized political leadership, such that even if the British had been doing better than they already were, it would be difficult to even arrange a true surrender of the colonies in one fell swoop. You’d have to get all thirteen to agree to surrender, and in reality that would have probably been a colony-by-colony affair, and unlikely to happen easily. Note that even the colonies that had their capital cities occupied didn’t surrender or make a separate peace with the British.
The third serious problem was how geography combined with the above factors acted as a “difficulty multiplier” in the British being able to do what was necessary to win the war. Waging war across the Atlantic Ocean is no small feat even in the year 2012 (see talk of whether or not the United Kingdom, easily one of the top 5 most powerful military forces on the planet and probably top 3, could recapture an island in the South Atlantic from a weak South American country), in the 18th century waging war across the Atlantic was massively difficult.
In the 18th century attrition rates were a lot higher than in the modern era, from ordinary camp diseases, from battlefield wounds that become fatal due to lack of antibiotics, and just to generally less discipline leading to more desertions and the like. Even though the British typically fared better in direct confrontations, in reality they didn’t ever do well enough to overcome the natural disadvantages. Every soldier lost to the British through enemy fire, infection/disease, desertion or etc had to painfully replaced from over the Atlantic Ocean. Some paltry number of Loyalists were raised to support the British, but their numbers were never enough to remove the real need of the British to continually resupply and reinforce across the Atlantic. The replacement cost of one casualty to the British was very high, the replacement cost to the colonists was much lower.
So just the distance involved made the geographical realities very much against the British. However, another large geographical factor was just the sheer size of the American theater. It was vast, sparsely populated, and most of the colonists were more or less self-sufficient at least when it came to staple goods. It was also not a highly urbanized 2.5m people, you could capture all the major cities on the Atlantic seaboard, but some 90% of the population did not live in the cities and more importantly weren’t all that highly dependent on the cities for survival.
The realities of European war rewarded risk taking and aggression, in the British predicament in the colonies even a rewarded risk–one in which you win the field, the ultimate costs of that victory probably actually outweighed any gain from actually winning the day. That was almost never the case in European wars of this time, capturing strategic objectives and winning the battles on the field were of paramount importance. Such objectives would expose the enemy’s most important holdings, their capitals and et cetera. Winning a battle in the field against the colonists wasn’t nearly as decisive, what they really needed to do was crush the armies themselves, so that they could no longer operate in the field. Unfortunately for them, they were never able to do this.
