We've displayed one or both on home pages in the past but after running tests and heat maps we now display neither for our largest eCommerce site.
That space is now taken by a large slider and other graphics pointing customers towards our most popular categories. The freed up space has been real nice for when we have sales or need to highlight a certain brand or category.
Since new products are no longer displayed on the home page I created a category for newest products and added it to all of our navigation menus. This has been much more effective for us (backed by analytics) rather than listing new products on the home page. All categories can be sorted by best sellers so that wasn't much of an issue either.
It's going to be different for everyone though. If possible test several versions and see what your customers respond best to.