Do __proto__ and Object.getPrototype of expose exactly the same functionality?

Do __proto__ and Object.getPrototype of expose exactly the same functionality?

No. .__proto__ only works on objects that inherit from Object.prototype. And Object.getPrototype doesn't allow to mutate the prototype.

Does the standardization of __proto__ in ES2015 negate the need for Object.getPrototypeOf?

You've got it backwards. ES5 Object.getPrototypeOf and ES6 Object.setPrototypeOf completely negate the need to ever use __proto__.

The Object.prototype.__proto__ accessor property is only standardised in ES6 for backwards compatibility and interoperability between implementations that need it. It's explictly marked as a web legacy feature. Check the note on Annex B ("…legacy features [for] web browser based ECMAScript implementations. [They] have […] undesirable characteristics and […] would be removed from this specification [if not used] by large numbers of existing web pages […]. Programmers should not use or assume the existence of [them] when writing new ECMAScript code. ECMAScript implementations are discouraged from implementing these features.")