Camera Lens: The Google nexus 5 features better lens than Sony Xperia Z1, hence you get bright lens with Google nexus 5; you get cleaner images at low-light condition, better color and contrast reproduction.
Sensor Size: The Sensor size of Sony Xperia Z1 is better, hence you get broad dynamic range with low noise and more details in your images compared to Google nexus 5.
Megapixel: You get more resolution with Sony Xperia Z1; hence you can take out high quality print-out with Sony Xperia Z1.
Image Stabilization: Google nexus 5 features Optical IS, hence you get clear / blur free images with Google nexus 5 in low-light situation.
Continuous shooting: Sony Xperia Z1 features fast continuous shooting speed compared to Google nexus 5.
Video: Google nexus 5 features Full HD Video recording @ 30fps on the other hand Sony Xperia Z1 features HD recording at @ 30fp.
Secondary Camera: You get better secondary camera with Sony Xperia Z1 (2 vs. 1.31 MP)
Processor: Google nexus 5 features advance CPU unit compared to Sony Xperia Z1 (2.2 GHz, ARM Krait 400 vs. 1.3 GHz, ARM Cyclone (64 bit)), you get fast clock speed + more cores try to finish the task faster, other benefit includes sharper screen resolution, smooth streaming HD video, quick loading of large image files and heavy graphic multiplayer games should be very smooth.
Weight: Google nexus 5 is light weight compared to Sony Xperia Z1. Hence travelling with Google nexus 5 is easier.
Battery: you get better battery life Sony Xperia Z1. 2,300 vs. 3,000 mAh.