First, Firefox is also open source. However Chrome will be running on the Webkit engine where Firefox runs on gecko. Webkit was developed by Apple for Safari but is based on the khtml engine which was developed open source from the ground up where gecko came from Netscape when they folded up and released their source code. Because khtml was always an open source project apple legally had to release their improvements back to the open source community so Webkit is officially an open source project that apple contributes to (and now google). Webkit is MUCH faster than any other engine available right now and gets a 100/100 on the Acid 3 web standards test.
So, in short it should handle every site better than Firefox and IE. IE is the worst performing browser across the board -security, stability, speed, resource usage, web standards- and is only good for the MS lazy web-designer websites which are disappearing from the net. Besides which I and all other web developers have to add special code to a website only for IE to render it properly. No other browsers have special requirements like this because IE is the only browser that ignores web standards and tries to insert their own. MS claims this will change with IE8 though.