I felt the out of Ship parts in Assault were a good idea but not properly executed. Both the landmaster and on foot parts made it just feel like an extension of the ship but ground based. The landmaster was alright but on foot it just felt like you were floating around.
If they remake the game with all 3 modes of transportation then I feel both the Landmaster and on foot experiences should feel more kinetic. Make the ride a bit more rough in the land master and on foot tighten the camera so it is closer to fox, give a 1st person perspective, and give the camera some shake. On top of that make the guns feel a bit more like they are guns and not turrets. And don't give fox so much health! It really annoyed me how hard it was for fox to die. But that may just be my opinion.
And also I agree that they should adopt a more serious attitude like the N64 StarFox instead of the more cartoony story lines that we have presently.
Multiplayer would be quite nice aswell.