Okay, I've been browsing the website of The Mojave Experiment, and found out what I already knew: Ubuntu still triumphs over Vista.
First video: Security
The Mojave Experiment brags about how Vista gets fewer malware infections than XP SP2 in the same time period. No kidding, anything would! Besides, malware coders probably get tired of dealing with easy stuff like Windows.
It also talks about parental controls. It wasn't clear to me in the video if Vista could block specific websites, but I know that Squid and Dansguardian combined on Ubuntu can. As for the restricted logon times, it would probably take a little more work to do the same thing in Ubuntu, but not much. Just make two scripts; one to disable and one to enable the child's account, and schedule them with cron, at, or gat (a front-end for cron and at).
Second video: Compatibility
I have not experienced compatibility issues with Ubuntu, but in my experience with Vista, "compatibility mode" doesn't work with any of the five to ten programs I've tried. XP's compatibility mode worked better for me than this - it had a success rate of about 50%.
As for the hardware, The Mojave Experiment talks about having the following statistics:
Cameras = 500+
Printers = 2000+
Media players = 150
As for Ubuntu, the numbers are less, but when you consider that you can set the cameras and media players to be read as a "mass storage device", I'm guessing it really would boost that number. Also, for any hardware, you could always just use "NDISwrapper" and use the Windows driver. Lastly, these are just the ones that have been submitted - for instance, the "Cases/Cooling" on the Ubuntu HCL only has 6 items - this is obviously far, far from accurate.
Cameras = 361
Printers = 212
Media players = Not specified
Third video: Organization
The Mojave Experiment highlights three things in this video: the search capabilities, the 3D Flip function, and the file previews.
I'd say that Ubuntu is a fair amount behind in the search department, way far ahead in the 3D effects department (via Compiz-Fusion), and on-par to slightly behind in the preview function.
Fourth video: Windows Media Center
Elisa (a download for Ubuntu) has all the features of the player parts of Windows Media Center, while MythTV has more features (according to what I have read) than Windows Media Center does for the recording side of things.
As for the "panoramic stitch", the photo he showed after the stitch was not panoramic - but you could do what he did or do a "panoramic stitch" in Gimp.
Fifth video: File Backup
Honestly, I can not speak about file backup on the Linux front: I have never used such features. However, of all the versions of Windows I have encountered, none that I have tried System Restore with have worked.
Sixth video: Gadgets
Ubuntu has gadgets of its own, though I have never used them.