Lets look at the Honda, IF (and this is a biggy) the previous owner(s) followed the maintenance schedule correctly, then the Honda MIGHT last a while longer. but being 16 years old, if something does go wrong then some replacement parts might be harder to locate. 109K miles in 16 years leads me to suspect that it saw mostly stop and go driving, Not always a good thing for cars.
Now the Dodge, plenty of them out there still running, maintenance parts should be more common to find, with 85K miles, it probably saw some highway miles, usually that's not considered too bad on a car, better then only city driving usually. I think that you should learn if that Dodge has the 2.7L V6 in it, I would watch that more then worrying about the tranny.
You could look at both vehicles, maybe test drive them AND while out and about stop in at a dealer (you did call them first, right) and have them give the car a once over to see what needs fixing.