They have different capabilities. For example, if you have a Samsung smart appliance or television, you can do a lot more with those with the new app.
The biggest advantage for Classic is in geopresence (many more options in Classic) and being able to use custom code.
SmartThings is in the middle of a big transition right now: new app, new hub, new cloud platform. It appears that the new app is intended to support custom code via the new cloud platform–which isn’t finished yet.
See the following thread for details on the differences (the thread title is a clickable link)