The crown prince was much more wordly and a great deal smarter than his father
Not smarter, quite to the contrary, but much more stable and reasonable - and very polite and diplomatic in personal dealings, able to win over people.
In the case of FF's assassination, he wouldn't believe in monarchial solidarity as Wilhelm II did. He knew how much hatred there was for Germany and Austria in Sankt-Peterburg, so he wouldn't expect Tsar Nikolay II to tolerate an A-H punitive expedition into Serbia - like his father did initially.
Bethmann Hollweg woudn't be chancellor under Wilhelm III, so anything else is difficult to predict. Is Bülow back? Or is Tirpitz chancellor? Or someone else?