Tales of Birds and Epiphanies

The Awakening and A Doll's House are indeed very similar.  Each has a wife and mother who is learning about herself and breaking away from what society tells her to do and be.  Edna and Nora are practically the same person - I still keep getting them confused.  Both women have husbands who are controlling and concerned with their roles in society.  In the end, the wives successfully get away from their husbands and are free from the life they had.
Of course, there are differences in the books - the most obvious being the way they escape.  Nora has an epiphany and walks out of her house.  Edna, on the other hand, escapes by committing suicide.  Though some people may say that suicide is the cheater's way out, I disagree.  In her eyes, she had no other options.  Her reputation had been ruined, and she had nowhere to go.  Another difference is the relationships Nora and Edna formed while away from their husbands.  Nora began to lean on Dr. Rank, seriously considering getting money from him.  She clearly did not love him; she just wanted his money.  It can be argued, though, that Edna loved Robert.  She had a relationship with him very unlike the one with her husband, and was experiencing a new sense of freedom with it.
Both books dealt with bird symbolism and freedom.  Nora's husband frequently called her his little "skylark," and Edna actually moved into a pigeon house.  Symbolism doesn't get much more obvious than that, folks.  But the meaning of the bird motifs differ: For Nora, she was her husband's skylark, while she was constrained in that marriage.  Edna's moving into the pigeon house was her big step towards freedom.  She had moved out of her husband's house into her own.
Overall, The Awakening and A Doll's House are very easy to compare, and even easier to confuse (especially when you've just watched Gone with the Wind.)  They're great stories about feminism that intertwine amazingly.