Neither one was really an innovator though. Both were salesmen at heart, with Jobs being more of the visionary type, good at inspiring others to invent things he could sell, and Gates being more of the ruthless bandit type, good at stealing things from others to sell and getting away with it.
I think Jobs was an innovator, but not a technician or engineer. He did have a vision of what he a a device should do, and how the public could use it, and then relied on others to make a computer, iPod, iPhone, etc, to make it happen. Originally, he used Wozniak to make the first Apple computers, then the Mac team, then multiple teams and Ive for the later devices. But in each case, it was his concept that was turned into consumer devices.