Personally I think the note 4 will make you forget all about LG... I've looked into LG phones but what made me not get LG G3 is seems like carriers was trying to give it away free under contract...
I started looking into reviews an people r saying that battery life is horrible an the phone overheats...
I bought Note 4 cause as of all Samsung Flagship phone they seem to hold up, I came from iPhone, an from my experience with my Note 4 after having it 3 weeks is amazing, The build quality is very nice Samsung really got that classy look and premium feel. It don't feel like a cheap phone like pervious Samsung phone that have all plastic. As for the screen I think the Note 4 by far is best screen on the market as of today but might change after 2015 flagship phones come out, battery life I can say is great. I've been getting about 17 hours with 6 an half hours on screen time per charge, an fast charge is a very nice feature! 0%-50% in under 30min.
Phones are honestly personal preference, depends what your going to use the phone on a daily basis. So do some research an see if it the phone for you?