I'm not that familiar with Islamic banking, but I do know it's forbidden to charge interest on loans. Obviously, common folks would absolutely love not having to pay back interest. It would also mean that the horrible Federal Reserve bank wouldn't be able to exist, because we are perpetually paying back interest to them for every note they print. Getting rid of them would be fantastic.
But it's difficult to have a healthy financial system without banks making profits. And if I assume correctly, Sharia law also prohibits gambling or stock trading, so I don't know if I'd want strict Islamic banking to takeover. Seems to me it would limit prosperity.
And I am not an expert, btw.

Canardo is the expert here.