In all given universe reincarnations, they suffered the loss of their father, sister, and home in a tragic house fire. Such event pulled the remaining bits of a shattered family together. That’s how the Moyaux family rolls.
So in addition to being twins and sharing an already close-knit brotherhood, they grew closer from sharing an experience of such magnitude.
Drastically different morals and hobbies honestly did little to hinder their relationship.
Edsel is adventurous, wild, an creative person with create answers to creative problems. He hates obligations and dishonesty, but enjoys his friends and the excitement within moments. Niko is refined, classy, a practical person with practical solutions to practical frivolities. He detests the idea of being tied to the truth of matters and emotional bonds, but manages to still hold a place in his heart for his family. In the end that mattered little because they still watched out for each other.
Socially, Niko is a charismatic pro and could get you to jump into an ocean if he damn well pleased, and Edsel blubbers around and prefers animals to people. Edsel thinks abstractly and in all directions, while Niko is logical and linear. Edsel is all about making due, using strategy, Niko is about getting more than what he has, using skill.
And on their somewhat different looks:
In DE: Edsel and Niko both became relatively well known for adventuring and film, enough for them to dye their hair and get some piercing to differentiate themselves from one another and keep their fans away from the other.
In Colorimetry: As a kid, Niko contracted a virus know as Chromaticism. It colored the once light-brown hair he and his brother shared a peculiar red, and it could potentially lead to mass discrimination due to the abnormal mutations to physical capabilities that the condition also posed. His brother was left unaffected by the virus. So Niko has just pretended auburn was his natural hair color his entire life and he liked to randomly dye it a few different shades as cover for when his hair dye started fading. And Edsel would dye his hair with blonde streaks to help make it look more like Niko’s was the more natural one. He was a weirder kid growing up anyways.
And so the two have always watched out for each other, no matter the circumstances. Also, on their 21st birthdays (In Colorimetry) Edsel has given Niko an Apache Revolver of his own design as a gift. So there’s that.