This is an awesome question and I'm excited to see what other people say. I'll start by saying that more than most wars, the First World War does seem to arouse the most nationalist sentiment among historians, even the normally dispassionate ones. In the English-speaking world, much of our World War One historiography has been produced by Brits. Many of these books are perfectly subjective. Hew Strachan's survey of the war, The First World War (2003), is very even-handed. One of his specific goals for the writing of the book was to remove the Western Front- (and British-) centricity of First World War history. As such, and because the book is so sweeping in scope (strategic, operational, tactical) Strachan doesn't really allow himself to get bogged down in the question of "who really won the war," or "which army was best." On the other hand, you have authors like Paddy Griffith (an author I quite like) who wrote his book Battle Tactics of the Western Front: The British Army's Art of Attack, 1916-18 basically in an attempt to claim that the BEF was the best army in France during the last three years of the war in tactics, strategy, and operational design. One of his central arguments is that the vaunted infiltration tactics generally attributed to Captain Willie Rohr and the German Army sometime during 1915 were actually a British invention and that the German Army copied them, not the other way around. As a counterpoint to this argument stands Bruce I. Gudmundsson's book Stormtroop Tactics: Innovation in the German Army, 1914-1918 which tells the more conventional story of the German Army as the home of cutting edge tactical development. He argues that the mission-oriented and decentralized German command structure and the self-supporting squad fireteam were innovations that were not to become standard practice in other armies until the Second World War.

I'll go ahead and offer my opinion as an historian at this point and then try and answer your central question. First though, why is the Great War such a theater for nationalist history of the "my army was better than your army" sort. Well, simply put, it's the World War where one side does not have the clear and accepted moral high ground. Getting anywhere near admiration of the Wehrmacht's fighting capabilities in the Second World War puts a lot of people on edge. On the other hand, the Germans in the First World War have a less clear-cut moral position. Much of the newer historiography I've read has tried to spread the culpability for going to war in 1914 among the Great Powers, if not outright absolving the Germans of any sort of immoral practices. As such, the sides are, I guess, more evenly matched in terms of historical support, if that makes any sense. Second, the tactical innovation of the First World War is truly astounding and it's understandable for historians to want to accredit that to their country and the army their fathers or grandfathers fought in.

But on to your question of whether the British Army was better than the other Armies in the field in 1918. Paddy Griffith, who I mentioned above with his very pro-BEF narrative of tactical developments, lays out a few reasons why the BEF has been denigrated in post-war tactical analyses. First, since the Vientam War, the US debate has generally spun more towards the German view of tactical innovation. "...In the US debate since Vietnam, was the idea that all German soldiers were almost always incomparable tacticians, from the lowest 'deeply professional and long service' NCO or stormtrooper, right up to the gifted Colonel Max Bauer, the fiendish Colonel von Lossberg, or the omniscient General Sixt von Armin... But can we really trust such a critique, in view of the fact that the Germans lost the Great War?" and further down, "A facile contrast can also be made between the slow British progress against strong defenses on the Somme and at Passchendaele, and the much faster German advance against weak defenses in the spring of 1918. However, one should add to the equation the devastating casualties ufferd by the Germans on the latter occasion, due to their almost total neglect of tactics, as well as the far faster and deeper allied advances which subsequently won the war. As at Appomatox in 1865, the tactical brilliance of the final campaign has often been overshadowed by the varied emotions arising from the war's end." He then goes on to accord to the BEF all the tactical innovations of the German Army. Griffith also claims that the early supporters of the tank are a main reason for history's less than favorable view of British tactics in the Great War. Pro-tank lobbyists had a vested interests in showing that the British Army's infantry tactics had crystallized and stagnated during the war and that only the tank had won victory in 1918.

I'll use Strachan to answer the question, though, since he's significantly more even-handed and broader in general. By 1918, the British had developed and were the best practitioners of "combined arms" warfare, which sought to combine infantry attacks with artillery, mobile fire support by tanks, and aerial observation and disruption bombing by airplanes. With the advent of better communications technologies, this combined arms approach would become the hallmark of modern warfare. The most decisive of these areas of development was in the field of artillery gunnery. At Cambrai, British gunners used curtain fire which sought to lay curtains of fire between German positions, essentially isolating them from communication or reinforcement. The bombardments were also less concerned with "preparation" and the days-long bombardments of 1916, but more with counter-battery fire and the knocking out of enemy guns. In terms of volume, although Germany had more guns than both the British and French combined in January of 1918, the British had pulled level by November through its high industrial output capability.

In terms of operational planning, the British had come up with (in conjunction with the French, I must say) the limited offensive, which was neither the bite-and-hold attritional battle a la 1916, nor the willy-nilly "advance as far as possible for as long as possible" of the Michael Offensive. The attacks were designed not to outstrip the reach of friendly artillery. Furthermore, British infantry outfits had modernized in terms of organization and technology. British battalions had gotten smaller since 1914 - 1000 to 500 - but also had more light machine guns and mobile mortars, and usually tank support.

By 1918, the British were on par with the Germans in terms of stormtroop tactics, and which army actually developed them first is a matter of national pride for some historians. They certainly better adopted the principles of combined arms warfare which would become famous during the Blitzkrieg years of 1939 and 1940. They had better operational design and were supported by allies with whom it had close contact and coordination. This cannot be said of the Germans, whose allies were a dying Austria-Hungary and a pan-Turkic crusading Turkey. At the tactical level, whose army had the best individual fighting men? That's a question I'm not going to tackle, mostly because 1) it's a can of worms, 2) I don't have as much experience with the BEF as I do with the German and Austrian armies and don't want to bias my answer and 3) I'm not sure it's a question which can be answered in an historical manner. I think it's more interesting and important to note that the armies throughout the war were evolving and learning from each other with a rapidity that's dissappeared from the popular perception of the war. Much more than a stagnant, stale war fought from trenches, the Western Front was a highly dynamic conflict in which armies and soldiers were forced to learn from each other and either adapt or die.

Sources:

Strachan, Hew. The First World War. Viking, 2003.

Griffith, Paddy. Battle Tactics of the Western Front; The British Art of Attack 1916-1918. Yale University Press, 1994.

Gudmundsson, Bruce I. Stormtroop Tactics: Innovation in the German Army, 1914-1918. Praeger Books, 1989.

The United States Army was inexperienced, and very few of it's forces managed to see battle. The German Army's doctrine (Stosstruppen) was deeply flawed, and they never managed to achieve a degree of combined arms operations equal to that of the Allied Armies. The French Army was qualitatively close to the BEF, but it's role was reduced due to casualties, and the BEF began to shoulder more of the burden from 1917 onwards. The BEF captured half of the prisoners and guns captured by the Allies in 1918, which the French captured a quarter, the rest being split between the Belgians and Americans.

Insofar as the German and American Armies are concerned, Hart is more or less spot on, and I'd say he is right to an extent with regards to the French, though I would give the French more credit than he gives them.