The most significant differences that I can think of:
-new IDE support HiDPI screens
-new Vulkan rendering engine that promise improved performance but it is yet to be confirmed how much improvement we are talking about. Told the new engine is coming in May.. Can be significant in VR/AR games.
-improved debugger that allow you to add variables to watch list and follow their values as you program execute and even change their values manually and see the result in preview
-code properties that allow you to expose variables to the IDE and change those values from the IDE even during preview, can be useful in large project to expose values that you want to play around with during development
-asset browser that include preview of your assets, can be useful when you dealing with lots of them especially songs and music as you can also play them in the asset browser, then you can drag and drop assets in to the scene editor but also the code editor which is generating Tier1 code for you to load it and include the path. Can be useful to get your content loading script up and running faster and in general to find what you looking for.
-in case you have been using the Visual Editor DLC or the Placement Editor in Classic, Studio has a better version included which offer you to:
---store scenes within scenes which can be useful to organize levels in large games for example cities, house interiors and dungeons..
---layers to help organize background, foreground, GUI elements on to different layers
---drawing sprites
---positioning using a percentage system
---better ways to reference individual sprites in the scene from code
---ability to group sprites to reference a group of sprites in the scene from code
..and more to come
And this is the most important imo, more is coming in Studio, Classic going to receive only maintenance updates, bug fixes from now on but not forever. I don't expect Classic to receive new updates longer than a year or 6 months from the release of Studio, it would make no sense imo.
Also all the visual editing part in Studio, is totally optional, so if you don't want any of the scene editing and asset management features you are not forced to use it, it is there for convenient only. If you want to do everything from code the "Classic" way, you can.