It appears to be an issue with the way subpixel rendering ends up working with Ubuntu and Arial. A suggested workaround is to make Arial automagically a size bigger when 12 pixel text is requested.
I couldn’t imagine it being so simple as putting a .fonts.conf in your home dir containing:
<test name="family" compare="eq"><string>Arial</string></test>
<test name="pixelsize" compare="eq"><double>12</double></test>
<edit name="pixelsize" mode="assign"><double>13</double></edit>
But it really is as simple as that. In human language, the XML file tells fontconfig to set the pixelsize of Arial to 13 when any program requests Arial with pixelsize 12. How beautiful.
I would guess there might be a way to tweak the subpixel renderer so that Arial doesn't appear too small at 12 pixels. If there's such a way, it's probably to be found on this crazy wiki page about fontconfig from archlinux. If someone wants to read that page and tell me what to do, I'd happily give them best answer.
For now, I just nuked the mscorefonts.
Here is another approach to getting fonts in Linux to look much more like those from Windows. I may update this answer tomorrow if I have time to try those suggestions.