Specificity is the word of the day. With a sufficiently specific reference you can style anything in Zen.
If you look at Page Source in your browser, you'll see that the featured products are in a div with a class of...
Code:
class="centerBoxContentsFeatured centeredContent back"
whereas the new products are in a div with a class of...
Code:
class="centerBoxContentsNew centeredContent back"
And all of that is inside a larger div classed as centerboxwrapper. So when you change that one you change both. Instead, change (add it if it's not there) the class centerBoxContentsFeatured. Apply whatever styles you want to it, and different styles to centerBoxContentsNew and you should be fine.
Note: the above will apply a style to each of the products independantly. If instead you want to style the block the featured products are in, all at once, there's an id you can use. The same div that is classed as centerboxwrapper is IDed as either featuredProducts or whatsNew, so you can apply your styles there to, for example, put a colored box around all the New products as a block, or a colored background behind all the Featured products as a block.
HTH
Rob