There are things which should be done server side (i.e. Express, not Angular), most notably user input validation - Angular, as it's client side, can be tampered.
Also, if you'll ever want to offer access type other than web app (i.e. mobile app), you'll probably need an API anyway - Express can do this, Angular don't.
Finally, database access - usually Angular app will need to connect to some kind of backend to perform CRUD operations. You'll either go with hosted DB like Firebase, or you'll end up using your own database. Latter scenario is more popular and you'll need Express (or similar) for that.
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