While I'm sure the grand plan is to eat Apple's lunch, they seem more focused on being better than themselves. I think they are onto something with the Surface line, they just need to keep iterating it. They also need to introduce a Surface product that the average consumer can afford--even Apple has done this with the Air line and the non-Pro line.
I have a MacBook now, but I'd love to go to a Surface Studio. If they can work to get up-to-date hardware in all of their offerings, and provide a $1k Macbook Air equivalent, along with a sub $2k iMac equivalent, they'll win.
Microsoft also has one other major hurdle. They lost a ton of ground they were gaining because they chose to force upgrades to Windows 10. I can actually get why they did this from a corporate perspective (Less OSes to support, therefore more money freed up to do other things), but as a user it sucks. They have to build an update to 10 that wins over the people they lost. They have to come out and say "Yes, we want your telemetry data, but we aren't going to force you to give it to us, so from now on, it's opt-in".
As far as Apple goes, I think they know they aren't innovating at the same pace. I think the headphone jack, the escape key, and touch bar are them trying to figure out how to innovate without Steve Jobs. I think Jony Ive is capable, but he needs room to fail to learn. Steve Jobs talked a lot about how as a company, you produce a lot of failures for each success. Steve Jobs was just much better at having many of those failures never see the light of day.
Either way, I don't care who the most innovate company is. I'd rather see them all trying to innovate, because the good stuff they come up with can only benefit the consumer.