They are both capable of violence and living a shared gangster life. Reggie is the more levelheaded one while Ron can be described as batcrap insane.
Tom Hardy plays as both Ron and Reggie Kray, performed with a tweak of facial expression and mild change on make-up. As far as biopic goes, other films such as Black Mass delivers a more in depth-look of the mafia life style, but Legend opts for a direct personal view of the brothers and takes full advantage of the lead actor. This movie is mostly dedicated to Tom Hardy delivering his excellent, albeit slightly and funnily schizophrenic, acting prowess.
It is true that glasses and change of hairdo can actually produce a different personality.