Probably Frederick living longer, as it seems to me he and his wife appear to have had a stronger relationship with the British Monarchy than Wilhelm. If personal diplomacy can avert Britain's clear alignment with Russia and France then the armed camps that were arrayed by the time WWI likely won't come into being. Delaying WWI could result in the continued existence of the German Empire.
I agree that a longer reign by Frederick III would have more positives than negatives . He may have been able to bring in more 'liberal" reforms that would take root in Germany, but remember that many of the other kingdoms, duchies, etc, within the Empire also have conservatism entrenched in their own local political and social structures. But some of the reforms brought in by Frederick III might be too strongly in place for a more mature even still conservative Wilhlem II to change when he comes to the throne. Also, time would be allowed for him to prepare for the job, as well as to truly formulate his love-hate relationships with his British relatives, and could fix some of the problems in place once he becomes Emperor.
I like this idea of a longer reign for Frederick III. I wonder how it might also be affected if his brother -in-law Edward VII could also reign longer and at the same time considering their mutual admiration for each other as well as similar political beliefs. For that matter, what if the more liberal leaning, (as compared to his father), Crown Prince Rudolph comes to power in Austria-Hungary as well? How does this all affect Nationalism, Imperialism, and the drive by many ethnic minorities for self-determination, especially in the Austro-Hungarian Empire in the pre-World War I years.