Thanks for the question!. I am happy to try to address your questions as best as I can.
The 3D geometry kernel and the sketch engine are quite different things. The geometry kernel in Fusion is very established. The sketch solver is bit newer. I think the biggest point to distinguish here is that there is a difference between some of the applications you named and Fusion 360, in that there is a sketch solver managing the degrees of freedom for every sketch entity. Sketch dimensions and constraints are the main tools that manage this within every sketch. Of course these tools go out the window if you are just inserting from another application.
Fusion is also always solving for the creation of profiles. Profiles are highly accurate enclosed areas denoted by the orange/yellow shaded area. These are often the basis for highly accurate 3D geometry (e.g. extruding a sketch profile).
You can also build a fully parametric sketch in Fusion 360 with relationship built on other geometry (e.g using projected sketch geometry). In the right hands, this sketch solver in Fusion 360 can make a entirely different sketch just by tweaking a few dimensions in the Modify > Parameters dialog.
Check out the forum post from jeff.strater in this discussion about the sketch solver. I think it highlights some the efforts underway really well.
https://forums.autodesk.com/t5/design-validate-document/what-s-your-fusion-360-performance-like/td-p...
If you are finding performance issues with inserted sketches, one thing you can do is to split up the entities into different layers in AutoCAD (or Illustrator - a bit of a guess on my part here). When you insert the resulting DXF file into Fusion using the Insert > Insert DXF command, if the sketch entities are in different layers this will put the entities into different sketches. This reduces the number of degrees of freedom and sketch entities that the sketch solver has to manage while editing any given sketch. This is probably the easiest way to manage performance issue with sketches in Fusion 360.
If you have a specific file to share, I'm happy to take a swing at inserting it into Fusion and making specific recommendations to improve performance.
I hope this helps. Please let me know if you have any questions, I'm happy to help.
Thanks,
Nathan Chandler
Principal Specialist