I have both the Verus and UAG cases. I like the Verus better due to slimmer and slicker feel. The UAG is cool looking and rugged, I liked it at first but I didn't like that the heart rate sensor is hard to get into due to not enough opening or groove unlike the Verus. Also there are mini plastic footing on the UAG that are kind of sharp to touch. I think these are for when you rest the UAG case facing upwards there is a space under it and the whole back of the case not resting on the flat surface.
With Verus, only con I see is it's a little bit slippery to hold since the back side is all smooth plastic, the sides though are rubber which does help in gripping the phone. Side by side though, I prefer the look of the Verus. I'm thinking of keeping both cases and use the UAG when I'm outdoors and need a rugged look (hiking, biking etc).
With screen protectors, I plan on not putting on one. I feel it takes away from the touch and look of it's awesome screen. I originally had S3 and removed the screen protector eventually. The screen is good that until today the S3 screen is scratch free, I take that the Note Edge screen would be the same if not better, so I'm skipping the screen protectors.
To OP, I just got my Note Edge last week, so about 2 weeks of use and so far I'm loving this phone. I decided to get the Note Edge after seeing the S6/S6 Edge and Samsung omitted replaceable battery option and expandable SDcard storage option. I assumed the Note 5 will be the same so I went ahead and get the available Note now. I originally planned on getting Note 4 but TMobile rep said I could return the unit if I don't like it within 30 days, so I went ahead for the Edge. I'm not returning this phone and plan on keeping it. Only CON for me, no Lollipop yet