Assuming she had no preconceived notions about how a computer should work (that is, wasn't already experienced with Windows and moving to a new interface wouldn't confuse her), I'd choose the one with the most stable networking implementation so that I could help her remotely. So Linux.

That said, I got Mom a Windows computer because she'd been using it at the office for years. I intelligently installed a VNC server on her computer so I could do remote help. In the couple of years that she's had it, I've been able to use VNC to fix a problem a total of once, I think, and the rest of the time I have to go over because her networking has gone haywire for no apparent reason.

Like Rob, I have a friend who thinks he's a computer expert. I guess I should more accurately say "had" a friend. I don't ever talk to him anymore because any time I ever talked to him, I got about 3 minutes of conversation and then I had to fix his computer for hours. I got sick of it.