Having worked at both places for ~4 years each, I would say Amazon is much more of a product company, and a platform is really a collection of compelling products.
Amazon really puts customers first. Their platform and organization are made up of small teams that own services with well-defined interfaces, accountable for customer metrics. All profits are reinvested, so resources and perks are scarce, efficiency matters, and management is tight. The platform emerged because internal teams thought of their infrastructure services as products with customers.
Google really puts ideas (or technology) first; it aims to hire the smartest people and rewards them for launching new things and solving complex problems rather than optimizing UX or making customers happy. Resources are ample and management is loose, so individual contributors can try new things with greater leisure. It's been compared to grad school. But simplifying customer experience is less of a priority, so the internal infrastructure was notoriously complex and hard to use. They're now learning to prioritize customers, but it's hard to change culture.
Of course, both companies are huge and diverse and evolving, so you'll find plenty of variance.
App Engine wasn't evidence of Google being a product company, nor does it exemplify the company's strategy. It was a grassroots project that for years didn't receive much leadership support, but was still allowed to launch and grow.