When you get a question of choosing News Feed or discussion board, the answer would be don’t use either of these. Below are reasons for not choosing these two.
News Feed or Site Feed
News Feed or Site feed is a default web part on out of the box team site template in SharePoint. It included text box with Twitter-style format where users can add text.
The common terminologies used are @ for tagine and #Moreover, also you can use Twitter characters like @ for mentions and # (hashtags) for topics. This includes images in the discussion. When @ character is used in discussion, the users will be notified by email.
Discussion Board can be included to the site just like out of the box web part. It is a SharePoint list equipped as a forum-style discussion unlike built-in Site Feed.
Just like other web parts, you can start the discussions/topics
but the terminologies like @mentions and #hashtags are not supported. We use SharePoint list, so you can view discussions in other views which are grouped and filtered respectively.
In SharePoint list you can set up alerts and it has Management/Moderation options which permits featuring of respective discussions.
You can even view the discussion under Featured section (view).
Note: Both News Feed and Discussion Board have limited features and not user-friendly. If you want to implement social features in your Intranet or Project teams sites, Microsoft has given Yammer, Office 365 Groups, Microsoft Teams, Planners which have all the social features, you can use any on them.