They're almost opposites when it comes to public image. Ballmer jumped in with immense energy and tried to make Microsoft look like a young person's company. I think that worked by helping draw younger talent to the company, but it wasn't very professional and may have hurt the image of Microsoft in front of Wall Street. But that's not really a problem if it still means successful products. However, under Ballmer's watch, we saw the launch of a diverse set of successful product, and flops. Remember that a lot of what has come out of Microsoft recently was likely part of Ballmer's work as Nadella is likely just getting into his plans.
I think Ballmer recognized that MS has a pretty strong footing when it comes to corporate clients. He seemed to push corporate products well, but also wanted consumer products. The later may have detracted from the stronger former, but as a result, MS pretty quickly became a household name. Between Xbox and the fact that people have started recognizing: 1 - that Office is not Windows and 2 - that their computer is not Microsoft (unless they have a Surface) really speaks wonders to how the general population has shifted its recognition of Microsoft, Windows and Office. Plus they now have the Surface, which seems to be doing VERY well. Unfortunately, it's unclear how that will impact companies like HP, Dell, etc.
Satya seems much quieter Ballmer, but I'm not sure that means his moves will be quieter. Microsoft needs to take big steps, and I think he sees that. I'm not sure how he will act, but it looks like he is enthusiastic about the company and it's products, but in a very different way than Ballmer was. Personally, I'm hopeful, albeit a tad cautious. There just hasn't been enough time or example to compare the two yet.