Are you looking for an objective reason? Or are you interested in leading, albeit entirely speculative, interpretations?

The question of why a religion took hold in any place or time--I would argue--is not a question that historians can (or should try) to answer. If you are still interested in speculative interpretations, I can provide a number of leading (and fringe) hypotheses, but speaking as a historian, I would say that your question is not one I or anyone else can answer.

It's sort of like asking scientist a question about anything supernatural.

If you were to seek an objective reason, the most likely candidate would be the fact that both Islam and Christianity went through phases of militaristic expansion followed by evangelistic conversion. Conversion by the sword was common in both religions, and both made a point of targeting elites (e.g., kings) for conversion. Because of the latter, both religions ended up being the religion of the elite at various points, meaning that it became a social gateway that limited access to upper mobility.

I'm sure all of the above were contributory. The main issue is that I can show you a hundred examples of other religions who were doing the same things, but never became world religions. That's why I'm weary of saying they are sufficient to treat a "why" question.