The answer is "actually, not a lot". These are very much iteration handsets, tweaking what was wrong with the S8 and S8+, but without adding anything majorly new or groundbreaking. The biggest change for both handsets is in the camera department , with the S9+ getting a dual camera setup (a first for a Galaxy model phone), while the S9 makes do with Samsung's new "dual aperture" camera design.
Here's a quick look at what's "better" on the S9 / S9+
|Galaxy S8/Galaxy S8+||Galaxy S9/Galaxy S9+|
|Display||5.8/6.2-inch Super AMOLED, Quad HD+, 18:5:9||5.8/6.2-inch Super AMOLED, Quad HD+, 18:5:9|
|Processor||Exynos 8895/Snapdragon 835 Octa-core, 10nm, 64-bit||Exynos 9810/Snapdragon 845 Octa-core, 10nm, 64-bit|
|RAM||4GB LPDDR4||4GB / 6GB LPDDR4|
|Rear camera||12-megapixel, OIS, Dual Pixel, phase-detection autofocus, 4K video recording||12-megapixel, OIS, Dual Pixel, phase-detection autofocus, 4K video recording / 12+12MP dual camera with dual OIS|
|Front camera||8-megapixel autofocus, F1.7 aperture, QHD video recording||8-megapixel autofocus, F1.7 aperture, QHD video recording|
|Storage||64GB internal, microSD slot (up to 256GB)||64GB internal, microSD slot (up to 400GB)|
|Software||Android 7.0 Nougat||Android 8.0 Oreo|
|Battery||3,000/3,500 mAh, Adaptive Fast Charge and fast wireless charging||3,000/3,500 mAh, Adaptive Fast Charge and fast wireless charging|
|Connectivity||4G LTE, Bluetooth 5.0, Wi-Fi a/b/g/n/ac, USB Type-C, 3.5mm headphone jack||4G LTE, Bluetooth 5.0, Wi-Fi a/b/g/n/ac, USB Type-C, 3.5mm headphone jack|
|Dimensions||148.9×68.1×8.0mm/159.5×73.4 x8.1mm, 152g/173g||147.7×68.7×8.5mm/158.1×73.8x 8.5mm, 163g/189g|
|Other features||AKG earphones, 32-bit audio, Bixby virtual assistant, Samsung Pay, IP68 water & dust resistance, fingerprint sensor, iris/face recognition, pressure sensor||AKG earphones, stereo speakers, AR Emoji, 32-bit audio, Bixby, Samsung Pay, IP68 water & dust resistance, fingerprint sensor, iris/face recognition, pressure sensor|
There is one other, significant change though; one which every user of the S8 / S*+ will be very happy about - the fingerprint sensor has finally been positioned *under* the camera sensors in the middle of the device. You know; exactly how everyone else did last year!