More reliable than girth, in judging tree age, is the way the bark changes as a tree gets older. This is different for each species. For instance red maples get shaggier, but tulip poplars and some oaks get 'balder' (smoother) near the base. Here I am standing next to an ancient oak that has balding bark.
The best way to judge a tree's age is by looking up. The oldest trees will be very tall -- having reached for the top of the canopy over many years. Relative height seems to be a better indicator of age than relative girth -- but exceptions abound in the forest, as elsewhere. Here is what an old tree over 100 ft. tall looks like:
Note how much greater the trunk volume is compared to the branch volume. (Taken with Photosynth app). To the discerning eye, however, it is the 'architecture' of the branches that tell us which trees are truly ancient. Look for tall trees that have fewer limbs, and with limbs that are thick and twisting. When you see "sinuosity" such as that exhibited by the tree below in the North Syracuse Cemetery Oak Grove -- then you know you are walking among the ancients.This tree could be 300 years old.