Does browsing privacy depend on what browser you use?

[cluelessignorami]

I use public wifi networks a lot (at school, at work, and otherwise), and I want to keep people from being able to spy on my browsing activities. If I switch browsers, from Internet Explorer to some less well-known browser that's harder to hack into, will it make any difference? Will that make it more difficult for people to spy on my browsing activities? When someone tries to access your browsing activities, do they have to be able to hack into the browser you're using to do that or not? If the answer is yes , then I guess the browser you use does make a difference. But if the answer is no, then maybe it doesn't make any difference. Which one is it?
Thanks

[Casper]

Yes and no.

Your privacy can only be affected via your browser by the sites you visit via for example Javascript, cookies and DirectX. There is a client-server communication between your browser and the website you visit, where your browser act as a client when you want a webpage and the webserver as a server.
People in your network cannot access your browser history via your browser.
However then can see what kind of webpages you visit by using so called man in the middle attacks. With MITM, hackers can retreive the messages you send to your accesspoint and read and modify them. These messages contain page request/passwords from you to a site. You can prevent them to read (most of) the content of your messages by using a Secure Socket Layer (SSL) connection.
If you go to google.com you can also type https://facebook.com htttps://twitter.com etc. you would be suprised how many sites accept this connection. In this was hackers can't read your passwords but still can see what pages you request.