Use Microsoft Graph to access data from services like Outlook, OneDrive, Azure Active Directory, OneNote, Planner, and Office Graph, with a single access token through a single endpoint. If you have an app using the individual endpoints and you want to take advantage of the Microsoft Graph instead.
Some features may be available on the individual service endpoints, but not yet on Microsoft Graph. We are working hard to bridge these gaps. If you require one of these features, you can use the individual endpoint in the meantime. Check the release notes for details on the Microsoft Graph features in preview and generally available.
You can refer to the figure to compare the difference between them:

I would also like to know what is the difference between the response we get after hitting both the APIs, and if there is any change in the
It depends on the version of API you were using and restrictively the type of data is under different namespace. For example, in the Office 365 REST API 2.0( Namespace="Microsoft.OutlookServices"), there are for navigate property(Attachments, Extensions, SingleValueExtendedProperties, MultiValueExtendedProperties) But in the Microsoft Graph 1.0( Namespace="microsoft.graph"), there are only two(attachments, extensions) and its property begin with lowercase. And the Microsoft Graph REST beta version add another two navigation property.
To get the detail information about these two endpoints, you can get the metadata like below:
GET: https://outlook.office.com/api/{version}/$metadata
GET: https://outlook.office.com/api/v2.0/$metadata
GET: https://graph.microsoft.com/{version}/$metadata
GET: https://graph.microsoft.com/v1.0/$metadata
And here is a page which help you choose your endpoint.