The two phones are nearly identical, except for the noticeably curved design of the Galaxy S6 Edge (hence the name). The company didn't do away with the fingerprint reader found in the Galaxy S5, which, was really just there for novelty, and to compete with Apple. The previous sensor required a swiping action, however the new sensor makes more “sense” and just requires a press. Might as well just copied Apple Touch ID from the beginning, guys. It also has a variety of uses now. It links with PayPal, the new Samsung Pay, Android security settings, and to unlock the device (Geek).
Other worth while mentions include a faster camera, still with 16MP, but a larger aperture of F1.9, as well as improved launch and capture speeds (Geek). As far as power and productivity between the two models, both smartphones feature Samsung's 64-bit octa-core processor, 3GB of RAM, between 32 and 128GB of internal storage, and runs Android Lollipop 5.0. The SD card slot found in the S5 is now gone, but there's plenty of connectivity going on- Wi-Fi, Bluetooth, and NFC (Digital Trends).
The biggest difference has to do with software running on the S6 Edge. It's curved display allows the option to show a bunch of notifications across the screen, as well as the option to flash a different color for each caller. Both the S6 and S6 Edge offer a 5.1-inch AMOLED display protected in reflective Gorilla Glass, a brushed-aluminum design, and boast 1,440 x 2,560 pixels (Digital Trends).
Perhaps some of these new features, but especially the design, will be enough to bring in an entire new slew of Android users, even for a dedicated iPhone fan. Picking between the two is probably going to be based on whether you really care about that extra curve in the display. Other than that, hardware, functionality, and added features are present in both. Pricing is still hush-hush, and both handsets won't actually be available until April 10th.