Alexander Watson says more about this in chapter 7 of The Cambridge History of the First World War, Volume II: The State:
The Germans were most sparing in applying the death penalty because their justice system was staffed by professional legal personnel and influenced more than that of other forces by civilian norms. Their courts’ concern with justice for the individual was bitterly criticised after the war by conservatives, who claimed wrongly that it had damaged discipline and morale.
In Military Executions during World War I, Gerard Oram argues that the German military code, dating from 1872, was
arguably the most liberal of all the belligerents of the First World War. Without doubt the construction of the state governed by law, or Rechtsstaat, played a large part in this. The law was more tightly constructed than the British code. Desertion, for example, was not as loosely defined as it was in the British code. Sentencing and the rights of soldiers were also written into the law rather than being left to the whim of the commander-in-chief. This caused some consternation to General Ludendorff and his staff, who clearly felt constrained by the nature of German military law
The table below is from Walker (chapter 7 - Table 7.1 Military executions, 1914–18.)
(asterisk in table) "America’s executions were all for non-military crimes (murder and rape). Ten soldiers were executed in France and twenty-five in the United States."
On the low percentage for US executions, Walker writes:
The lenience of the US military was solely due to President Wilson1, who commuted all death sentences for military crime; only murderers and rapists were executed. Other forces embraced the death penalty as a deterrent more wholeheartedly.
1 In US courts-martial, 24 death sentences for desertion were imposed. All were commuted by Wilson. See Charles Glass, 'The Deserters: A Hidden History of World War II'
None of the aforementioned sources cite any figures for desertions, perhaps because such numbers can only be guessed at to a large extent. With reference to the British and German armies:
Both...had a rather difficult time defining desertion and devising effective deterrents for it. Often commanders were reluctant to report it, because a high desertion rate reflected badly on an officer's leadership.
Source: Robert Weldon Whalen, in a review of Christoph Jahr, 'Gewohnliche Soldaten: Desertion und Deserteure im deutschen und britischen Heer 1914-1918', The American Historical Review, Vol. 106, No. 5 (Dec., 2001)
This 1914-1918-online. International Encyclopedia of the First World War article does offer some figures, but they are too limited for us to draw any firm conclusions on comparative desertion rates among the belligerents. We may accept, though, that
For Britain, Germany and France, deserters - with all the caveats linked to judicial statistics that are difficult to interpret - appear never to have numbered more than 0.5 percent of men in uniform before 1918.
Although the number of German executions was low (despite the mass desertions - up to 180,000 - in the summer and autumn of 1918), those convicted were more likely than their British counterparts to have their sentences carried out: 48 soldiers executed out of 150 capital convictions, or 32%. The British, on the other hand, 'only' executed 11% of those convicted. Nonetheless, the relative leniency of the German military code during WWI is in stark contrast to that of WWII when, under the Nazis (who blamed deserters, among others, for Germany's WWI defeat), the
total number of death sentences handed down for desertion were about 22,750 with a probable 15,000 executions (65 percent) carried out.
Source: David H. Kitterman, 'Review: The Justice of the Wehrmacht Legal System: Servant or Opponent of NationalSocialism?'. In 'Central European History, Vol. 24, No. 4' (1991), citing Manfred Messerschmidt and Fritz Wullne, 'Die Wehrmachtjustiz im Dienste des Nationalsozialismus: Zer- storung einer Legen' (1987)
The WWII British army, on the other hand, did not execute any soldiers for desertion.
Also worth noting is the WWI Italian execution rate, much higher than that of any of the other belligerents. This was due to the "harsh" military code and its strict implementation by the Chief of Staff of the Italian Army, Luigi Cadorna.
The Italian military code was passed in 1869 and was based on its Sardinian predecessor (1840). It was particularly harsh, particularly with its very broad definition of desertion. During the First World War, Cadorna, the Italian Commander-in-Chief, made ample use of this in imposing a brutal disciplinary regime on his troops. Military crimes, which included desertion and insubordination, were punishable by being shot in front, but so-called ‘dishonourable’ crimes such as treason or murder were punishable by being shot in the back. Sentences were normally carried out within twenty-four hours, but sentences passed by extraordinary drum-head courts – including death sentences – were carried out summarily and ‘ad modum belli’. This allowed Cadorna to apply strict discipline from the moment of Italy’s entry to the war. In July 1915 he warned that ‘every soldier . . . must be convinced that his superior has the sacred duty to shoot all cowards and recalcitrants immediately’.
The Wikipedia article on Cardona notes that:
David Stevenson, Professor of International History at the London School of Economics, describes him as earning "opprobrium as one of the most callous and incompetent of First World War commanders."