Fire Emblem games do differ somehow. For example I am playing FE 4 right now (Awakening is FE 13, Path of Radiance FE 9). That game only has 12 maps, but each of those is so large that it could be 4-5 chapters in most other FE games (including Awakening). From the story perspective, FE 4 is probably one of the most epic ones, telling a story of war that spans two generations (it was the first and only other FE with a marriage system) and has huge armies fighting one another.
Most other FEs are only taking place on either one continent and/or a short amount of time. Awakening is a bit special and is probably the FE with the most customizable content because of the ability to train every character in skirmishes and change their class so they start at level 1. But that doesn't mean other FE games are bad. I really like Path of Radiance and especially Radiant Dawn, Sacred Stones is sadly way too easy, but the game itself is still quite good.
I would suggest that you just try out some of them. The overall gameplay is pretty much the same in the whole series (with some one time features and others, like the weapon triangle, that were common in the series after their first appearance).