I 'd say go with the Avalon between those two. The Taurus has a timing chain driven water pump that you will be guaranteed to replace before 200,000 miles. It's not a cheap endeavor, either. If they blow, they dump coolant into the engine oil. Toyota makes way better transmissions than Ford, and proper maintenance will keep it going a really long time. Between expensive water pumps and transmissions, there's $10,000 saved. The Avalon will run laps around that Taurus when it dies and still go another 200k+ if you take care of it. 

Since you keep your vehicle to at least 200,000 miles go with the Avalon.  Justin Shepherd is correct in his assessment and I have nothing to add there.  As a bonus, the Avalon at 200,000 miles will still have much better resale value than the Taurus.  Rarely do people have buyer’s remorse or regret buying a Toyota despite the higher price tag. However, that is not the case with Ford whose quality/reliability has degraded over the years.

Toyota all day.

I think that Taurus would easily get you 200K miles without any big problemos. They're of course famous for water pumps that go bad and leak into the oil pans, but that isn't a 10K job and could be done preventatively if you're that worried about it.

I can't imagine spending near 10K more for an Avalon just for that Toyota badge to greet me on the hood. You didn't mention trims... I would go and test drive both and buy whichever one you like the driving experience of more, instead of basing soley upon the oval on the hood. The Avalon is a better vehicle but it's up to you to decide if it's worth that much more money.