I'm not entirely sure about why Ubuntu would see one USB versus another other than perhaps file system type or limitations in the guest addition USB handlers.
The solution I use is to mount the USB drive (or partition) as an OSX volume and then access it from Ubuntu via VirtualBox. In other words, a bit roundabout compared to mounting the USB drive directly in Ubuntu. But this approach has an additional benefits - both OSX and Ubuntu can see the same drive and can use it for easily sharing data between host and guest.
If using the USB partition frequently in Ubuntu and in OSX then should make the partition case-sensitive. An optional bonus is encrypting the partition if you're into that sort of thing.
OSX: Mount the partition normally in Finder.
OSX typically automounts a USB drive to /Volumes ... Example: /Volumes/MyUsbPartition.
See also: http://osxdaily.com/2013/05/13/mount-unmount-drives-from-the-command-line-in-mac-os-x/
OSX: Share that volume via VirtualBox Manager
Add '/Volumes/MyUsbPartition' as a ShareFolder (with full access).
I enable "Auto Mount" and "Make Permanent" but if only mounting it termporarily, don't make it permanent.
This means the "shared folder" will appear automatically in Ubuntu as /media/sf_MyUsbOsxPartition (permissions: user:root, group:vboxsf).
NOTE: Requires "Guest Extensions". See selected answer for http://askubuntu.com/questions/22743/how-do-i-install-guest-additions-in-a-virtualbox-vm
Summary: Ubuntu APT install virtualbox-guest-additions-iso (places ISO in /usr/share/virtualbox).
Mount this as a CD (sudo mount /usr/share/virtualbox/VBoxGuestAdditions.iso /mnt)
Run the install (./VBoxLinuxAdditions.run)
Login as your normal user (example: "MySelf")
Add user to the vboxsf group (usermod -aG vboxsf MySelf; # Or edit /etc/groups directly)
Only need to do this once since will remain for future cases
At this point the drive can be accessed directly from either OSX or Ubuntu.
The downside is the extra step to add it as a shared folder in VirtualBox. This isn't generally a severe drawback in my use case but your mileage may vary.