For me, I always preferred having Windows on my home or office computer. But I have always used Linux when it came to running a server. Not to say one is better than the other. They are both good platforms that have been around for quite some time. But I myself always felt Windows servers were more well known for running networks in the workplace. Linux servers have been much more common among web hosts probably because of the savings in cost. Think about it for a moment. You are a web host and you need to decide what platform you want. Windows or Linux? The Windows Server OS is rather pricey to begin with. Then you need to protect it with antivirus software. And because it's a "server", you cant just use any antivirus on it. It has to be antivirus software for "servers". That usually costs almost as much as the OS does. By the time your done doing the math, you will find that running Linux is a much better solution for the hosting company and would save you tons of money. That savings could then be passed onto the customers and they will greatly appreciate it. This is why you may often find Windows hosting plans more expensive than linux hosting plans.
So to answer your question, neither platform is probably better than the other. They are both good in stability. It is just moreso personal preference. As for one being faster than the other, Linux is less resource intensive. But if the server has tons of ram and a really good processor, it may not make to much difference anyways.
As for the web host, I would have to agree with everyone else. There is no such thing as unlimited space. You cannot go to the store and buy a hard drive with unlimited disk space on it. The plan should be advertised as unmetered space and bandwidth. Not unlimited. Unmetered means that you can use as much disk space and bandwidth as you want as long as it can be supplied. Saying that those items are unlimited means they are overselling which is never a very good thing in the hosting industry because you aren't getting what you paid for. I would suggest finding another host.