I own one of each -a 2019
I own one of each -a 2019 Forester and a 2020 Outback. Here is may take on the differences.
The Forester has cleaner bumpers, with restrained use of plastic cladding. It also has the widest tailgate opening of ANY Subaru at 48.6 inches. It also has physical buttons to disable the annoying Auto Stop/Start and Collision Avoidance System. On the Outback, the driver is forced to use go through the touch screen menus to do the same thing.
The Outback roof height is a little lower, but that is an advantage when washing the roof or loading cargo on the standard luggage rack. The cargo floor offers more load space. Only the base Forester offer more total cargo area, those with the sunroof lose space due to the moonroof assembly that is standard on Premium, Sport, Limited and Touring models. All Outbacks have nicely finished alloy wheels. The longer wheelbase provides a smoother ride. The Outback also has a nice heads up display that alerts the driver to lane drifting. The Forester beeps at you and you must look down at the instrument cluster to see what it's complaining about.
The engine in my Forester runs more smoothly than the Outback, but this is likely due to production variances. Both engines come from Japan and have the exact same specs.
They are both great vehicles, but I prefer the Outback.