The major difference between these two is that the US government, led by Pres. Roosevelt, was much more proactive about preparing for and trying to get involved in WWII. This is in contrast to Wilson's policy of trying to avoid involvement in WWI.
Once WWII started in Europe, FDR took many steps to help the Allies and to get the US ready in case it got into the war. The most obvious of the steps that were meant to prepare the US for war was the fact that the US started drafting men into the armed forces in September of 1940. This was the first time that the US had ever had a draft when it was not at war. By contrast, there was no draft and no major buildup of weapons in the period between the start of WWI in 1914 and the US entry in 1917.
The most obvious similarity occurred once the US had entered the wars and was trying to get ready to fight effectively. In both wars, the government set up agencies to help ensure that materials needed for the war would be available. These agencies did things like working with businesses to make sure that military materiel (rather than civilian consumer goods) were produced.