This is the week that the Mozilla organization is expected to unveil what may very well be the most significant half-point release in its history: the 3.5 edition of the Firefox browser. While Betanews tests confirm the new version literally blows away its own predecessor in terms of speed, operating two-and-one-half times faster in page rendering and functionality on average, your own eyes will tell you it's a much faster browser.

And those same eyes will tell you that Google Chrome is already a much faster browser, by virtue of a supremely fast V8 JavaScript engine that its developers have been refining since version 1 made its debut last year. In recent Betanews tests, the Chrome 3 beta has overtaken the stable release of Apple Safari 4 as the fastest Web browser publicly available, posting a performance index score that's 83% faster than Firefox 3.5 RC3 on Windows XP SP3. So while Firefox has made extremely significant gains, it may take open source developers until version 4.0 for it to catch up with Chrome in the speed department.

Firefox's developers tell Betanews that version 3.5 makes up for that gap in the functionality department, by providing tools and resources that Chrome currently cannot match. We decided to test that theory for ourselves, with a new series of tests that pits the two most viable choices for alternatives to Microsoft Internet Explorer against one another in everyday, real-world tasks.

Chrome users have already come across that browser's "Incognito" function, which brings up a window exclusively for pages whose history and cookies will not be tracked permanently. Firefox 3.5 formally inaugurates a similar feature with "Private Browsing." Yes, we know there's stuff that folks don't want their bosses knowing they're looking at. But the other typical use-case scenario involves folks who are shopping for gifts for other members of the household, and they want those gifts to be secret.

There are certain things that do need to be remembered during an online shopping experience. You find things, you compare them, you make notes, you do research. So our question was, is each browser capable of remembering what it needs to remember and forgetting what it needs to forget?

Our first simple test begins with the "shopping cart" (if either browser fails this test, it shouldn't be shipped). Most shopping sites can maintain a running shopping cart list for their customers, even when those customers aren't logged in. In order for sites to do this, it needs to maintain some kind of session state, which requires a cookie. So this does mean that Incognito / Private browsing maintains cookies, although they should go away after the session ends. At least that sounds about right.

To make sure this is indeed the way these features behave, I started shopping carts on the Web site of one of my favorite tech gear suppliers, Xoxide.com. Here, as is the case with most sites, you don't have to log on as a returning customer to launch a shopping cart. Xoxide is having a Fourth of July sale, and I like to check out the deals in case I want to build yet another computer. My wife might not appreciate yet another glowing receptacle of whirring electronic mayhem adorning our already wire-strewn household, so I begin by shopping incognito with Chrome 3.

Chrome lets you run a standard window alongside the Incognito window, and marks the latter with a little "cloaked spy" icon in the upper left corner. As I start building a little near-term history, my first fear is that it will have some impact on the non-private history outside the Incognito window. So in the main Chrome window, I pull up Xoxide, and I discover that window does not perceive the same shopping cart. That's good.

Next, is there any chance that the history buffer in the main window would "remember" the URL for checking the shopping cart from the Incognito window? With Xoxide, as it turns out, there's one URL for checking the active shopping cart -- and having already done that in the main Chrome window, I've messed up my test. So I have to rig a similar test using a different retailer: Newegg.com. With Newegg, the shopping cart's URL begins with a different prefix, secure.newegg.com. When I begin typing "secure" in the main window's address bar, it does not offer to complete my URL with the shopping cart name from the other window. More good news.

Firefox 3.5's Private Browsing mode works a bit differently: You can't have both private and non-private windows open simultaneously. You have to exit Private Browsing mode (which is marked with the phrase "Private Browsing" in the title bar) to return to standard mode. With Private Firefox, I started a fresh Xoxide shopping cart and chose something new. Then to check whether I left any trail, I exited Private mode and checked Xoxide in the main window. Shopping cart is empty, and there's no trail of it in the history buffer of the "Awesome Bar," which is what I expect.

Next, I return to Private mode. Here is where the "experience" changes: When you exit Private Browsing mode in Firefox 3.5, that is when you erase your trail. Your shopping cart ceases to exist at that point, which truly means Firefox works as advertised.

Next: The trail unravels…