Not all sticks are worthy of being aged and the same is true for pipe tobaccos.
Only the full bodied sticks age the best. All sticks will age to a point, 2/3 years and show improvement, but will then they begin loose their flavor profile. The fuller bodied stick, with the highest grades of tobacco, will age and improve for long period of time 15/20 years and much longer. Opus X, Paul Garmirian, Ashton VSG, etc. are examples of cigars that will age well over long period of time. Also, Puros tend to age better than blends.
The same is true with pipe tobaccos. Aromatic tobaccos do not age well at all, nor do tobaccos containing Latakia. Burly, Virginia, Orientals & Perique ages very well and can become amazing smokes with age.
It's a lot more complex than what I have said, but what I have said is a very good rule of thumb!