Changes to a given cigar's taste and aroma due to its age is difficult to predict, as everyone has already pointed out.
With the brands that I store, it has been my experience that over the first couple of years of aging, the cigar usually becomes bolder, with more complexity. If you have a cigar that initially tasted "young," age can help get rid of the ammonia and will usually result in a more sweet cigar. Even though age can help develop a cigar's taste and aroma so that it becomes more nuanced.... I've seen too much age take away a cigar's strength and pepper.
I'm not sure what the appropriate age target is, but I have some La Flor Dominicana Double Ligero (original band) that have been aging for several years, along with Tatuaje Tainos and they are better than the newer production releases... because of age. I occasionally will compare them to the newer releases... yum, yum.