I'm not sure there. Obviously Germany would clash with the other European powers because of conflicting intrerests and domestic politics. A different persona at the helm would not be able to avoid that. But internally, in terms of her political stability and constitutional order, the person of Wilhelm II mattered much more. The continuing destabilisation of the cabinet and Reichstag, the enormous loss of prestige for the crown, and the need to go in for crowd-pleasing grand ideas to fill in for the hollowness of all political institutions go back pretty directly to Wilhelm. Germany had a chance to grow functioning political institutions the way she grew functioning civic ones. But it would have taken an emperor with better people skills and a steadier hand.
Of course there is no way of telling whether Henry would have been that man. He had some very problematic sides. Still, not being his brother might be enough to give his country a chance of a sounder government, a better diplomatic corps and a less dramatic style of conflict resolution. The Reichstag really was everything an emperor could have wished.