I do enjoy Awakening more than Fates, simply because I found it more enjoyable to play. I played Birthright and Revelation, and both were somewhat boring and lacking in the story. I did managed to get attached to some of the characters, but not many. I found it difficult to care about what happened to some of them, because they just didn't mean anything to me. Awakening's characters are better in my eyes, and I grew attached to many of them. The ending was also better - quick and dirty, defeat Grima once and that's it. The need to defeat the boss multiple times can be done well, but it wasn't in the case of Fates.
Don't get me wrong, I still enjoyed Fates. I just think it tried too hard to be like Awakening (Birthright and Revelation did, anyways - I hear Conquest is more like previous Fire Emblems) and didn't do it well.