Hi carlover, u ordered your z1 from telco or from other shop? I am contemplating to switch from my current s3 to z1 
		 
		
	 
Samsung S3 is a good phone but Sony Xperia Z1 is a much more better phone. In real fact there no phone that are perfect. But this are the run down on why Sony is better.
Software
Samsung TouchWiz Loaded with All Samsung Widget and more
Sony Xperia Loaded with Only Sony Customize Icon and Simple Layout
In this Sony have the lesser issue for long run. Very near to Stock Rom.
Camera Features
Every company have their own camera UI
Samsung come with standard and appealing camera shoot 
Sony have that in their module too but added in more fun to it ie. Long burst or 2 sec with many images shoot and the latest AR effect which are very interesting too.
Keyboard Wise
Personally it down to individual usage as there are many keyboard that can be downloadable 
Samsung keyboard is quite somehow not as accurate. Will miss if you type fast. 
Sony keyboard is fast and accurate. Nearly identical to IOS.
Opening and Closing of apps
Samsung transition are smooth but when firing out app you will feel the Zzzz transition somehow everywhere.
Sony transition are smooth but it much more straight forward without and Zzzz effect.
SONY equal Simplicity