I have used AppEngine, off and on, for many years. The advantage is getting auto-scaling and robust data stores automatically. The disadvantage is some degree of technology lock-in and that you can host less expensively using a provider like OVH or DigitalOcean.

EDIT: another good thing about AppEngine is that the 'free tier' will let you run a low traffic site for free, or very inexpensively. IBM's Bluemix is another service with a generous free tier.