Both ともあろうものが and まじき seem to be used for say that a person in that position shouldn't act in a certain way because it is not appropriate. However, I'm not sure if I understood them correctly. Could somebody provide me some examples to grasp the difference existing?
「Xともあろうもの(者)が」 is used with X that designates someone or a class of people, to express a strong disapproval/disappointment. 「一家の主ともあろうものが仕事もしないで遊び歩くなんて」 (how can a head of a household can go out and have fun without even having a job!?) 「者」 is a formal sounding word, and I find myself more comfortable using 「Xともあろう人が」.
Apparently 「まじき」 historically had a lot wider usage but in modern Japanese it's really only used as 「あるまじき」 to mean "unthinkable", so I think it basically means the same thing as 「ともあろうものが」. For example, 「仕事もしないで遊び歩くなんて一家の主にあるまじき行いだ」