Unfortunately Photoshop doesn't support any kind of a subpixel rendering. Nor does any other Adobe software—with the exception of Dreamweaver. (Well it is not exactly Dreamweaver's technology, as it just renders the HTML and then passes the text for the operating system to be rendered.)
The suggested workflow may be that you create and slice your design in Photoshop and then open it in Dreamweaver. If the design needs further corrections you could have the file simultaneously opened in Photoshop, do the changes, save, and refresh the view in Dreamweaver. Add the final, real copy in Dreamweaver. You could also replace Photoshop with Fireworks; or even start wireframing in Fireworks → continue in Photoshop → publish through Dreamweaver. (It comes clear why the Creative Suite editions are usually bought in bundles, doesn't it?)
If the design looks different in Dreamweaver's preview than in browser(s), that is an another, unfortunate, matter (and I'm not talking about just the typography but the rendering as a whole). The sooner you can elevate from Photoshop to live demo—be it via Dreamweaver or not—the better. I do wish Photoshop would have subpixel rendering powers (but at the same time hope it won't be introduced in CS6, or at least hope I will be rich by then)!
Just a side note: ClearType is protected with 10 or so patents, so exactly the same rendering is not probable. Also it is worth noting that OS X uses different rendering (Quartz) by default and so do the graphical interfaces in linux distributions.