On the surface, Nest would seem to have been the perfect fit for Apple. Nest makes very innovative products that can interface with those of Apple, and its founder and several top staffers are former Apple employees.
If you measure innovation prowess by patent activity, IBM is actually the winner, and has been for a long time. Big Blue, for the 21st consecutive year, was awarded the most U.S. patents and broke its own annual record with over 6,800 in 2013. Google and Apple trailed well behind at Nos. 11 and 13, respectively.
In spite of the Nest purchase, it doesn't appear that Google has any clear advantage over Apple on the innovation front.