In general it is not the OS that would make your internet connection slow. It depends primarily on your ISP and your available bandwidth for upload and for download. Cable connections are generally fastest but vary greatly depending on how much bandwidth you neighbors are using at the time; DSL is slower; and dial-up is extremely slow.
Some issues that ARE under your control are things like the packet-size. Files are broken up into "packets" of information and encoded with a checksum; when that packet gets to your computer, it the checksum doesn't match then it needs corrected or retransmitted - lots of retransmissions may make it seem like your connection is slow but really it is transferring data but it had to resend the same packet 3 or 4 times. To tweak these settings you might try the freeware tool from speedguide:
SG TCP Optimizer. You may find that if you use the optimal settings in the general and advanced tabs you may notice slight improvement.