There's lots of good stuff going on under the hood in Opera 12. First and foremost, plugins now run in their own separate process, so crashes can be isolated without affecting the rest of the browser. They've also fiddled with how tabs are loaded, improving startup time when you have lots of tabs open.
Opera 12 is now available in 64bit as well, for both Windows and Mac, but 32bit will remain the default for now. Apart from experimental (default: off) support for hardware accelerated WebGL and page-loading, the interface can be rendered using the GPU as well. These are experimental features turned off by default, and it'll depend on your graphics hardware and drivers just how stable it will be.
Furthermore, Opera 12 supports CSS3 Animations, cameras, HTML5 drag and drop, and, like Chrome, now also has a resource monitor so you can see what's hogging up resources. Of course, there's, a lot more in here than just these features.