I had both
And personally i would say i like the XperiaZ a lot better than the SGS3.
The overall-look and feel is just amazing, the SGS3 in comparence felt cheap, and i really really hated the blue-ish screen of the SGS3,
although overall it had better viewing angles than the XperiaZ.
Camera: In dark conditions be it in video or picture-mode, the SGS3 surpasses the XperiaZ, in daylight the Camera of the Xperia-Z is better, except for Macro-Shots, those are better on the SGS3 too.
Sound: The sound that the microphone of the XperiaZ records (videos, telephone) is really crystal-clear compared to the SGS3 one.
The Headset/In-Ears are better on the Sony as usual, but even with other/better (Sennheiser/Audiotechnica/AKG)-Headphones the sound out of the Headphone-Jack of the XperiaZ is better than that of the SGS3
The Buildin-Speakers therefore are better/louder on the SGS3.
If you should purchase the XperiaZ is really up to you, in my location they are actually really cheap to get, so probably yea.
Although the Xperia Z1 Compact might be a better upgrade.
The Z1-Compact has a lot better Battery-Life a better processor and would be overall (in my opinion) the best upgrade, its not as expensive as the Z1/Z2 but on the other hand has superior hardware and battery-life compared to the XperiaZ.
But its really your decision, i can't make a decision for you
Hope it helped.