ineron Welcome on the forums!
Unfortunately there is no clear migration path going from 1.9 to 4.x. We have had to redesign a lot of the core in order to make sure we would not have to get to this stage again where we would have to introduce breaking changes to the structure and format that SA 1.9 uses.
The engine has changed, so in order to "upgrade" you'd have to replace each of your pages with the new mark-up of that same/related element. We tried very hard to visually stay true to what SmartAdmin represents and as such the layout has not changed that much. With that I mean that the aside is still there, just as the header and footer.
If and when time allows we could discuss internally about writing a guide in getting your 1.9 projected converted to 4.x but a migration scenario is unfortunately not possible without investing time in moving over said parts to your existing project. Apologies if this is not what you wanted to hear but we have had to go to great lengths in creating a true successor to the theme and unfortunately this could not be done without sacrifices, upgrading is one those paths.
Hope this helps,