This is a good forum for any Flash Pro questions. Did you know that in both you can set different workspace layouts? You would be able to get Animate to be laid out like you see in CS6.
A few versions ago Flash Pro was rewritten as a 64 bit application, but CS6 was before that, and so it won't perform as well on your PC as a modern app would. So it's more about CS6 being slow than it is your PC.
When you're watching an animation in the main IDE there are a lot of panels that are being updated. They don't need to be updated when doing a publish preview.
You can use the F4 key to toggle all panels off and on. Try using that to see if the animation then plays smoother.
Ok Will try this
Hey, I'm just replying to tell you that changing the layout of CC was a great idea! It runs as smooth as intended.
Happy to hear that! I'll mark my answer as Correct. You can unmark it if you disagree!