Design
The Galaxy S3 has dimensions 136.6 x 70.6 x 8.6 mm (5.38 x 2.78 x 0.34 in) and weighs 133grams while the Galaxy S4's dimensions are 136.6 x 69.8 x 7.9 mm (5.38 x 2.75 x 0.31 in) and weighs 130grams. The Galaxy S4 is smaller in dimension as compared to Galaxy S3 inspite having a 5'' screen. Samsung has increased the screen size by reducing the size of the bezel.
Display
The Galaxy S4 packs a gorgeous full HD display with pixel density of 441ppi. Galaxy S3 has a 4.8inch display with 720x1280 pixels and ~306ppi. GS4 is protected by Corning Gorilla Glass 3 while the later is protected by Corning Gorilla Glass 2
Specifications
GS4 is powered by the Exynos 5 octa in some regions or a Snapdragon Processor clocked at 1.9 ghz in regions mainly where 4g network is available.The GS3 is powered by the exynos 4 qaud core processor clocked at 1.4 ghz. GS4 has 2GB of RAM while its predecessor has only 1GB of RAM.
Features
The big difference between Galaxy S4 and Galaxy S3 is the addition of Hand gestures and Air View. Samsung has also upgraded the camera from 8 megapixels to 13 megapixels. the Camera app in S4 has features like 'Dual Camera','Sound and shot','Drama Shot',etc.
Differences between Galaxy S3 and Galaxy S4