Hi Baltimore -- welcome
First make sure you have the most recent patch...
To answer your question, if two cities have the same improvements, and the same types of units and same quality of troops, it does not matter.
In your example, you may have a tough time holding onto an older city because it had built up more culture points. Cities with strong culture are more likely to "flip" on you. (That is at least one of the factors).
I usually build a temple in recently conquered cities as quickly as possible.
I think it is good advice in regard to guarding against culture flips to attack border cities first. If you have strong culture improvements in your own border cities, this will give you a little protection in holding those cities, plus push your boundries out further. You'll also get the benefit of a connected road/rail network to bring up reinforcements quicker.
Somewhere on this site, is a very helpful article about the factors related to culture flipping.