There are a few things that you can do with fetch and not with XHR:

• You can use the Cache API with the request and response objects;
• You can perform no-cors requests, getting a response from a server that doesn't implement CORS. You can't access the response body directly from JavaScript, but you can use it with other APIs (e.g. the Cache API);
• Streaming responses (with XHR the entire response is buffered in memory, with fetch you will be able to access the low-level stream). This isn't available yet in all browsers, but will be soon.

There are a couple of things that you can do with XHR that you can't do yet with fetch, but they're going to be available sooner or later (read the "Future improvements" paragraph here: https://hacks.mozilla.org/2015/03/this-api-is-so-fetching/):

• Abort a request (this now works in Firefox and Edge, as @sideshowbarker explains in his comment);
• Report progress.

This article https://jakearchibald.com/2015/thats-so-fetch/ contains a more detailed description.

fetch

• missing a builtin method to consume documents
• no way to set a timeout yet
• can't override the content-type response header
• if the content-length response header is present but not exposed, the body's total length is unknown during the streaming
• will call the signal's abort handler even if the request has been completed
• no upload progress (support for ReadableStream instances as request bodies is yet to come)
• doesn't support --allow-file-access-from-files (chromium)

XHR

• there's no way to not send cookies (apart from using the non-standard mozAnon flag or the AnonXMLHttpRequest constructor)
• can't return FormData instances
• doesn't have an equivalent to fetch's no-cors mode
• always follow redirects

The answers above are good and provide good insights, but I share the same opinion as shared in this google developers blog entry in that the main difference (from a practical perspective) is the convenience of the built-in promise returned from fetch

Instead of having to write code like this

function reqListener() {
    var data = JSON.parse(this.responseText);
}

function reqError(err) { ... }

var oReq = new XMLHttpRequest();
oReq.onload = reqListener;
oReq.onerror = reqError;
oReq.open('get', './api/some.json', true);
oReq.send();

we can clean things up and write something a little more concise and readable with promises and modern syntax

fetch('./api/some.json')
    .then((response) => {
        response.json().then((data) => { 
            ... 
        });
    })
    .catch((err) => { ... });