Can you give us an overview as to why you're giving up on the Edge? What's better about the others and more importantly the Z3?
It's pretty much software related. It has a consistent GUI aesthetic that sticks to Androids material footprint to the point where elements are very Nexus like, but then offers all the customisation we come to expect.
But in doing so, it manages to keep its memory footprint low resulting in amazing multitasking performance which means in day to day use the device feels as fast or faster than devices that benchmark higher or feature newer processors.
It honestly feels snappier than my Edge in every day use and the edge was and is exceedingly snappy. However I have had significant issues regarding App refreshes on the S6 Edge due to aggressive ram management (a consequence of a dramatically more bloated under the hood OS). The Z3 often runs at 1/3 of the memory when booted compared to the S6 Edge and the affect for me is the Z3 keeps apps in memory longer and far more of them resulting in apps always ready when I go to them compared to the S6 Edge which will often reload/refresh content on me.
The Z3 battery isn't approaching 6+ levels but for me it's been utterly consistent, whereas my S6 Edge I was never able to get more than 3-3.5 hours SOT (yet others here routinely manage 5-6, sadly I just never got that).
The 16gb storage on the Z3 is low but the fact I can bolster it with micro SD has meant that hasn't been an issue.