I have actually lived and worked in Muslim countries.
I think a reason a Christian might convert to Islam, at least at the outset, is because it seems much simpler. A simple declaration that there is only one God, and Muhammed is his prophet. Coupled with the relative simplicity of the five pillars (okay, six if you count Jihad) it can appear a much simpler, more straightforward alternative to Christianity.
Mind you, I learned that Islam is much more complex than I imagined, with a very rich tapestry of competing theologies, even within what we consider the two big factions, Sunni and Shiia. Obviously, this can lead to a great deal of bloodshed, both within the "boundaries" of Islam and directed against the infidels or apostates (who they refer to as "takfiri").
Of course, the social pressure a involved and the history of conversion (to live in a dimi status, pay a jizya, etc, or shed your old religion for societal and material comforts) come into play as well. It's not a simple story.
But you can find some similar trends in the history of Christianity as well, for example, Charlamagne's treatment of the pagan Saxons, or the conversions of Danes to gain favor with Alfred's Wessex.
Conversions, or their successes or failures, don't prove anything about who is right. The perceived gains (whether other worldly or in socio economic terms) play a huge role.
Added by edit:
Also, keep in mind that the convert does not have to "reject" Christ, but revere him as the prophet Isa upon conversion. Makes it a bit easier, I'm sure.
Edited by Wollysaurus, : No reason given.
Edited by Wollysaurus, : Autocorrect is the enemy
Edited by Wollysaurus, : No reason given.
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