I really enjoy the edge display. It means that my home screens are a bit more free since all of my favorite apps are in the edge display. I also like the Samsung camera app as the shutter and most controls/options were moved up to the edge freeing up the main display. I can look at the weather without turning on my phone's display, see any notifications, control music (or any media) playback, etc. I don't think it's essential to the Note experience but I do like it. My fiance has a Note 4 and likes my Note Edge but she still prefers having a traditional, flat display. The Note Edge is a bit thicker than the 4 and the battery isn't quite as big but I can still power through the day and night on a single charge without issues, I'm not bothered by the added thickness, and the Edge display doesn't slow down the performance of the phone compared to the Note 4.
The only negative aspect that I have encountered is a lack of cases. You are pretty much stuck with $10 no-name cases from Amazon/eBay, a case from Verizon that sucks (don't get it), 1-2 other options from 3rd parties that can be pricey, or a rather craptacular flip cover from Samsung (I went with a $30 UAG case). Other than that, I have had nothing but positive experiences with my Note Edge and I hope Samsung releases a Note Edge 2 that keeps the functionality of the edge display (unlike the S6 Edge).
Just some food for thought: the Note Edge is nearing its mid-life cycle (or has already hit it). It was released 5 months ago (unveiled 7 months ago) and odds are high a new/updated version (or at least the Note 5) will be unveiled in another 5 months. If you aren't in an absolute rush, you may want to hold off until Samsung's event in September. My general rule of thumb when buying devices is to get them within the first few months of release and to avoid something if it is within 5-6 months of being updated.