Ballmer was stuck on the old ways. I was connected to a team that had made iOS office apps but Ballmer blocked because MSFT jewel apps on Apple meant Apple would gain marketshare over Windows Mobile. That team was fairly pissed and some folks quit.
Nadella was leading cloud division at that time, but they were not getting the firepower to go against AWS. Azure succeeded despite Ballmer. Nadella clearly saw Cloud was going to be the next big revenue firehose.
Ballmer closely held onto Windows walled garden. His bet on acquiring Nokia and Skype had spectacularly failed. Android and iOS had won, they entirely lost on Windows Mobile.
VSCode had just started but it was seen as an experiment and the sentiment was it could absolutely not jeopardize actual Visual Studio. Linux was seen a competitor to Windows.
Under Nadella, he saw an entirely different Microsoft. He was playing bets on the future, while Ballmer held onto the past. The game had changed.
Nadella didn't care about Windows walled garden. He wanted Microsoft on every platform where developers and Enterprises were. VSCode wanted to cannibalize VS go for it. MSFT apps on iOS go for it. Linux on Windows, go for it. All of MSFT switches to git, to for it. Acquire github and cannibalize Azure pipelines, go for it. Use chromium base for Edge instead of mshtml, go for it. Nadella made good bets over and over again. Ballmer doesn't have the same record.
Nadella + Scott Guthrie went all out on Azure to be #2. The infra spend alone was in billions. Remains to be seen how OpenAI bet pans out.