What do you mean by saving scenes? You can create HTML5 Canvas content which are pretty small in file size. The thing that's going to take the most amount of space is images and sound files.
If you're talking about a 3 or 4 minute animation with music with intent for saving the file for general distribution, if that clarification helps at all?
My professor seems to be weighing the decision of having us animate in HTML 5 or Actionscript format.
Both are small in file size so it shouldn't matter what you pick. Even with an animation that's 3 to 4 minutes, images and sound files will take the most amount of space.
If it's just an animation to show people, ActionScript files have some advantages (3D rotation, Stream sound sync, more filters). If the animation has to play in Safari on an iPad, then you would have to use HTML5 Canvas or WebGL 2D.