You might be interested in a few previous threads on the Jewish side of your question:

• Why has the population of Jews remain relatively constant throughout the years? - 3 comments, over 1 year old.
• A flaired user gives a summary of factors that significantly constrained the Jewish population throughout history.
• Proselytizing in Judaism - 3 comments, over 8 months old.
• A flaired user discusses several notable instances of conversions along with some details on the Jewish attitude towards conversion.

You might also check out:

How did Christianity go from a small, hated cult to the state religion of the Roman Empire? What made it so different than the hundreds of other small cults throughout the Empire?

and /u/talondearg 's followup post in Why did Christianity, and not another contemporaneous cult, spread so rapidly within the Roman Empire?. The followup post goes through some of the other religions of the time, including Judaism, in brief.

I'd argue because Catholic/Orthodox Christianity and Sunni and later Shiite Islam (as opposed to Gnostic Christianity, Kharijite Islam, Nestorian Christianity, etc. etc.) were able to grow so large because they controlled states. Over time, the areas that they controlled adopted their religious practices. New areas often took religious practices as a "package" of civilizational advances, including technology and "civilized culture". Romans weren't proselytizers, really, but areas under Roman rule adopted more and more Roman cultic practices, to choose an easily understandable example (and some peripheral religious practices made it back to the Roman center--including Christainity). See my answer to Why isn't didn't Sri Lanka convert to Islam the way Malaysia and Indonesia did? for my general perspectives on this sort of mass conversion.