^ the last answer especially should be pertinent. In short, if the British Army is anything to go off of, more soldiers suffered from shell-shock in WWII than in WWI. This makes sense both in terms of the size of the armies involved and the intensity of combat, and in terms of the better means of diagnosing it.
I'm not a historian, but I can address this more from a scientific perspective. If someone else can supplement this from a more historical perspective, that'd be great.
Soldiers didn't suffer from stress disorders less in WWII as opposed to WWI. Shell shock is more of a contemporary term to the Great War, when people believed it was caused by physical trauma to the brain due to exploding shells, but the phenomenon predates it and continued past it under different names. Shakespeare's "Henry IV" has the following passage,
O my good lord, why are you thus alone?
For what offense have I this fortnight been
A banished woman from my Harry’s bed?
Tell me, sweet lord, what is ’t that takes from thee
Thy stomach, pleasure, and thy golden sleep?
Why dost thou bend thine eyes upon the earth
And start so often when thou sit’st alone?
Why hast thou lost the fresh blood in thy cheeks
And given my treasures and my rights of thee
To thick-eyed musing and curst melancholy?
In thy faint slumbers I by thee have watched,
And heard thee murmur tales of iron wars,
Speak terms of manage to thy bounding steed,
Cry “Courage! To the field!”
There is also an example of it in the diary of Samuel Pepys, a survivor of the Fire of London, and that of Charles Dickens, who was rather severely affected by a railroad accident he was in.
While it isn't a historical source, one specific example of a PTSD sufferer from WWII that comes to mind is from Stephen King's novella, "The Body" which was made into the (AMAZING) film, "Stand By Me." Teddy's father, "stormed the beach at Normandy," but was very affected by it, nearly burning his son's ear off by putting it to the stove, and spent time in a sanitarium.
Wikipedia claims the apparent increased prevalence of combat-related PTSD in WWI compared to WWII is due to the greater rates of participation and implies a relationship to the increased risk of trench warfare, but unfortunately the claim is uncited.
The underlying phenomenon is what's currently generically known as post-traumatic stress disorder (PTSD), but is also known by other terms such as combat stress reaction in the military. When exposed to acute stress, animals undergo what is called the "flight or fight" response, mediated by the sympathetic nervous system through adrenaline (epinephrine) and noradrenaline (norepinephrine) released by chromaffin cells of the adrenal medulla, with NE playing a particularly important role. In PTSD, individuals react strongly to stressful, traumatic experiences, but not to stressful, non-traumatic experiences such as doing math problems by having this same response activated. Stress also results in the release of cortisol from the adrenal cortex, which both acts to mediate the stress response by raising blood sugar and blood pressure, as well as having a negative feedback role to turn off the stress response.
Individuals with PTSD have a number of differences, such as differences in cortisol levels compared to healthy individuals. More recent research has also implicated pituitary adenylate cyclase-activating polypeptide (PACAP), an activator of a G-protein coupled receptor that strongly stimulates secreting cells over a longer period of time by raising cyclic AMP levels in the cell as opposed to action potentials generated by activation of ligand-gated ion channels activating voltage-gated ion channels, which are very fast and very short. This may contribute to severity and duration of a PTSD attack. Some individuals with PTSD have higher circulating PACAP, and PACAP receptor expression is regulated by estrogen, which may explain the increased risk of PTSD in women.
sources:
http://www.ptsd.va.gov/professional/PTSD-overview/ptsd-overview.asp
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3181587/
http://www.nature.com/npp/journal/v38/n1/full/npp2012147a.html