Someone may have covered this already, but the #1 reason to have LTE in my opinion, is for a live data connection, while you are on a phone call. THis is the one feature ATT always brags about in their commercials. I am on the phone a ton and I also use my Google Maps to get to business meetings. Can't do both at the same time, if I don't have LTE.
Having a good hotspot in a business meetings is nice too. On 3g, sharing your hotspot to a few people makes it unbearably slow, but on LTE, you won't have any performance issues. Honestly though, I am likely going to get a 4g LTE tablet and use it for a hotspot. Hotspots tends to shread batteries, so having a tablet sized battery is the ultimate way to go.
Pretty much everything I get on Verizon now is going to require LTE. Dual core... not so much needed for what I do. I don't phone game anymore, since I have a tablet. Nothing else on my phone needs 2 cores. A year or two, I'm sure everything will require 2 cores, but I get new phones every year.