The DSLR looks quite a bit better in all of those examples, however maybe that's me looking as a photographer and seeing the background blur from a larger senso

The DSLR looks quite a bit better in all of those examples, however maybe that's me looking as a photographer and seeing the background blur from a larger sensor, better dynamic range and color, less highlight clipping, less noise, less processing 'smoothing' things, and so on. In reality none of that really matters for day to day photos, I take casual photos to have memories of places and people, and a smartphone does just fine for that.