Both use the standard GNOME trio of Applications, Places, and System for menus, with a limited selection of available applications and only minor variations in the arrangement of items -- for example, Ubuntu places a virtual terminal under Accessories while Fedora uses System Tools. However, in general, the differences in the desktop are minor. Admittedly, Ubuntu has simplified the GNOME menus slightly more than Fedora has, but this is an ambiguous advantage at best, especially since the simplification does not extend beyond the top level in the menus. Drill down, and part of the time you're going to encounter a few long sub-menus.
Still, the departures from standard GNOME that do exist are largely in Ubuntu. Working within the distribution rather than within the GNOME project, Ubuntu has rewritten the notification system, making it more useful, but also more obtrusive.
Ubuntu has also given the corners of the desktop specific functions: the top left for menus, the top right for log off actions, the bottom left for showing the desktop, and the bottom right for the trash can. Another Ubuntu innovation is the MeMenu, which attempts to create a centralized place for managing social media accounts and chats.
Undoubtedly, the largest difference in Ubuntu defaults is the placement of the title bar buttons on the left and the elimination of the window menu. This arrangement leaves a broad space on the right of each window's title bar, which in another release or two might be filled with some other useful information.
Yet for all the discussion of this arrangement, the worst that can be said is that it is initially awkward, while the best is that you can quickly get used to the change. Despite all the attention lavished on the change, it really doesn't affect your computing for better or worse.
Neither the latest Fedora nor Ubuntu strays very far from their shared GNOME roots in software selection. Both include the standard GNOME productivity applications, such as Firefox for browsing, Evolution for Email, and Empathy for messaging.
Each distro does include some applications that the other doesn't. For example, Ubuntu includes Computer Janitor and Gwibber, while Fedora boasts Network Manager and its ABRT (Automatic Bug Reporting Tool). Yet, generally, the differences are not vast.
The greatest difference is that, because Fedora uses Shotwell for image management and Gnote instead of Tomboy for a note system, it does not depend on the controversial Mono framework. These decisions seem to have been made to help free space on the Live CD, but those who disapprove of Mono will probably welcome them.
If anything, the most important difference in the distros' selection of productivity software is that Fedora includes only free software. If its users want to use Adobe Flash or Adobe Acrobat, they have to look elsewhere, and not in the Fedora repositories. The same goes for proprietary NVidia drivers and the MP3 codec.
Ubuntu, though, focusing on ease of use, has a looser policy, warning users of the disadvantages of proprietary software, but including it in repositories if the free software alternatives are weak or non-existent. Its Hardware Drivers tool in the Administration menu is essentially designed for managing such proprietary exceptions.
Yet, in the name of usability, Ubuntu does provide a link to the libdvdcss2 library for viewing videos. Although, like Fedora, it declines to include the library in its repositories because of its uncertain legal status in many parts of the world.