The Acura MDX and Honda Pilot are mechanically identical, so the maintenance and repair costs would be the same for either (if you're not at a dealer).
But I would be very cautious about buying a 12-year-old vehicle (2004 model) to transport your large family. My first concern would be that an older vehicle would not be as safe as a newer model. The other issue is that even the most well-built, high-quality vehicles (such as the Acura MDX) may require pricey repairs as they rack up the years and miles. Finally, on the subject of maintenance, I also would consider some alternatives to the Honda/Acura that doesn't require periodic timing belt replacements. If you do buy an older Pilot or MDX, make CERTAIN that the timing belt has been replaced! It should be done every 105k miles or 84-months.
As for alternatives, my personal favorite is the Mazda CX-9. It is larger than the Pilot/MDX and has more legroom in the 2nd and 3rd rows and also has the most easily accessible 3rd row. It was introduced as a 2007 model, but got a larger engine (3.7L vs. 3.5L) and nice performance boost the very next year. So I would look at 2008 and newer. It comes in three trim levels- Sport, Touring and Grand Touring (GT). The Touring and GT have standard leather, the Sport is the 'base' model with cloth. The CX-9 has been very reliable over the years with only one significant problem area- the transfer case on high-mileage AWD models tends to fail around 150k, give or take. Stick with a FWD model and you'll be fine. I found 2008 and 2009 Touring models with less than 110k miles and clear history reports for under $10k! FYI- I have a 2012 GT that I bought new and I chose it over a new Pilot or new MDX!
The other possibility that I really like is the previous-generation Nissan Pathfinder. A 2008-2009 SE or LE with leather and under 125k miles would fit your budget, but they're not quite as reliable as the Mazda or Honda/Acura.