Besides the fun factor of a curved screen and having 2 screens in 1, personally I think the best part is not having your texting, web browsing, emailing or video watching session interrupted when an existing calls comes in. The notification appears on the edge and you can choose to answer, reject or ignore.
I also like how notifications appear on the edge. Useful when you are waiting for the 2FA code to come in via SMS. Just quickly type the digits as you read it. No longer have to worry about forgetting the code after reading it.
Wish the battery life was better though.
That is the only and BEST benefit of owning an Edge. I have my Note 4 friends regretting their decisions. Like who wants to be interrupted in the middle of something good, right?
Battery Saving
1. If battery life is a problem, there is always the ultra power saving mode (use this mode when you are desperate for juice, cuz it will disable a lot of apps and it takes a while to enable and disable it); and extra battery packs.
2. The Edge does feature a removable battery.
3. Also, switching off wireless radios MANUALLY when they are not in use. WiFi, NFC (search Settings > NFC and sharing. I recall this is to be switched on - by default), BT, Location (GPS. Most apps do not use this. But if you are using apps with maps features, just turn it on before the system prompts. Duh

), Mobile data, etc.
4. Plus, you may also wish to not use the fancy clocks for the edge screen when you have your smart cover on.
5. Additionally, you may wish to enable blocking mode during the wee hours of the day (i.e. 12am-6am) to conserve even more battery.
6. Alternatively, there is airplane mode, but just remember to turn it off when you are awake.