I know America was in the UN but not the LoN, but I asking about more structural things, in terms of their charters, their powers and their organization.
One of the larger differences is that the League of Nations had no teeth, it had no military force of its own to physically put down an aggressor. The League of Nations provided that if an aggressor would not stop it could use military force but it having no force if it's own made it an empty threat. A nation would have to volunteer it's military but that means that nation would be declaring war.
Members of the UN volunteer troops to UN command, that allows the UN to have teeth when needed( like in the Korean War)