You are going to have to be more specific. Are you using the same versions of libcurl and PHP on both boxes? Are all other parameters exactly the same?
If the answer is no, I'm not surprised.
Additionally, the network environment might affect it, e.g. firewalls, transparent proxies.
Try to get it working from the command line on this unix server.
You should definitely enable all notices, warnings and errors, log them, and post any which seem relevant get if it's not obvious how to proceed on that basis.
Mark