The egg or kamado style is more for the BBQ purist. Have had a kamado for 2 years, and love it. I can do a 12 hour cook at 205 degrees with charcoal in below zero temps because of their thick (think insulated) shell. With a kamado you also have the ability for extremely high temps. I can get over 700 degrees, which will cook the best pizza you've ever had, or the best reverse sear steak you've ever had. It's a steep learning curve at times, but is a heck of alot of fun too.
Pellet grills are simple, like a crockpot that adds smoke. Kamado or egg is very challenging, the hardest part is learning how to maintain and get the correct temp. Both produce food that tastes good, with a good operator. It can be a struggle to maintain temperature on a cold day with wind with a pellet grill. There are very good kamado grills other than a big green egg too, for a lot less money.
That being said, I am now shopping for a pellet grill, going to go with a Rec tec or a yoder. Traeger is crap now, sold out to China, cheapest components of almost all pellet grills now. Green Mountain and Louisiana grills are much better than a traeger. With a pellet grill, you just set the temp and go watch tv. Sometimes that's ok too. Read some reviews at amazingribs. lots of good info there.
Good luck!