As MagKnightX said...
Your operating system has almost nothing to do with the speeds of your bandwidth (upload/download speeds). Neither does your CPU, RAM, Video Card, or most other pieces of hardware.
Your speed is probably 95% connection (what you pay for), and 5% (or less) equipment. Unless you've screwed up your equipment, failed to update drivers, or haven't restarted your shit for the past few years, your speed is likely just what you're paying for.
Most broadband services have different tiers of service. Mine for instance, offers packages of 768kbit, 2mbit, 4mbit, and 6mbit down speeds. (PATIENTLY waiting for a fiber connection)
The way they're labeled though is a little strange. Without getting technical, your actual download speed will be (usually) 10-20% of the connection speed. (So on my 6mbit connection, I generally get 600kbps to 1.2mbps down speed. It hasn't changed at all since I switched OS's, and hasn't changed since I upgraded from a 4 year old to a new computer...it's all in what you pay the ISP for.