As Winston Churchill said in his account of the Eastern Front in WWI, 'the Unknown War': "In the West, the Armies were too large for the land; in the East, the Land was too large for the Armies."
In the West, the high concentration of forces in such a small area meant that strategic and operational maneuver were virtually impossible. In the East, fighting took a form that would have been familiar in the Franco-Prussian War, the form that people had expected would characterize future wars: Big, Bloody and Decisive. The distances were far too great for extensive trench warfare, and this was the same in WWII.
Lambert, Tannenberg and Lodz in 1914; the Carpathian Offensives, the Gorlice-Tarnow Offensive and the Great Retreat in 1915; the Brusilov Offensive and the Romanian Campaign in 1916; the Kerensky Offensive and the subsequent central powers counter attacks, Riga, and Marasesti in 1917; and Operation False Flag in 1918, were all characterized by maneuver by infantry and cavalry, with artillery in support.
It's also worth noting that the stalemate on the Western Front did not continue as long as is generally believed; to quote a man who was there, Lt. Charles Carrington:
"The Great War on the Western Front began like most other wars ... when cavalry were employed on horseback and battles were short and sharp. It then passed into a period of stalemate, when infantry and guns burrowed underground and hammered at one another in prolonged trench to trench battles. In reality this period was not so long as has been generally supposed, the lines were rigid only in 1915 and 1916... during 1917 bomb fighting in the trenches gave way to shell hole warfare, and in 1918 to open fighting... in which tanks and cavalry played a large part."
By 1917, the Franco-British Armies had developed the means to break into German defensive positions at will. The Germans in turn, were shifting away from the linear, static trench defenses that had brought them near to disaster at the Somme, and were adopting an Elastic Defense in Depth.
The fighting in 1917 was very much open warfare, NOT mobile warfare. Fighting was no longer solely of a positional nature, but involved maneuver on a small unit level, flanking-and-firing on positions. An illustration of this comes from the bunker/pillbox and shell hole fighting at 3rd Ypres; Australian units actually began to request more Lewis Guns, less grenades.