The last mile is loads more efficient with online shopping, but all the miles before that are worse -- rather than stores buying densely packed pallets you have a monumental amount of additional packaging being added, and the items are optimized in trucks as best they can be given upwards of 90% empty space in their boxes. Since truck fuel economy is only weakly dependent on weight this winds up using a ton more energy.

I don't have hard numbers though, which makes it hard to answer questions like "do the last-mile efficiencies outweigh other inefficiencies?"