The first thing to consider when analyzing characters like Tom and Laura, who are siblings, is whether the central problem of the story equally affects both, and in which ways. That is the easiest way to extrapolate differences and similarities.
The pervasive issue that permeates the Winfield family is the trauma of abandonment, which has resulted in a degree of self-confinement, guilt, and frustration. These are the first commonalities that are evident between Tom and Laura.
Tom, the narrator of the story, is Laura's brother. His nature makes him a prolific reader, a poet, and a dreamer. Yet, he is unable to engage in any of these three behaviors because he is the main provider of the family, a role that he needs to fulfill, whether he wants to or not, after his father unabashedly abandons the family home.
Tom's precarious situation makes him engage in different forms of escapism ranging from drinking, to going to the movies, to writing poetry, and spending time alone at the fire escape. This latter behavior suggests his desire to escape his current situation. Tom's only hold is his love for Laura, his fear for her safety, and the loyalty he feels toward his mother, Amanda.
The self-confinement that comes as a result is basically the fear of moving ahead and letting go. This is what keeps Tom stuck at his job until the day when he makes the final and most important choice of his life.
Laura is Tom's sister. Just like Tom, she has been affected by the abandonment of her father. While not directly affected, she can empathize with her mother, Amanda, who is not only humiliated and hurt by such nonchalant abandonment, but is also left in a hard situation trying to fend for the family alone.
Laura has a physical condition that has been blown out of proportion by Amanda's overcompensating ways. She merely limps, but her social anxiety, her extreme shyness, and her inability to feel normal inside her own skin, make her think of herself quite horribly. Laura cannot even stand being in public, and gets sick when attending her course at business school, to the point of quitting. Like Tom, she has found a method of escape via old records and her glass menagerie.
The glass menagerie is to Laura what the fire escape is to Tom. In Laura's case, the animals represent her state of mind, fragile and transparent, and her personality, pure and rare. Laura also feels an attachment to her mother that makes her want to please her in every way possible. Just like Tom, she has a need to escape. Unlike Tom, she is too afraid to do it, and reverts to having her escapism become a normal part of her life.
Tom and Laura are essentially good children to their mother, they are good with one another, and they love each other dearly. They are both overwhelmed by their mother's abrasive behavior and by their father's disgraceful abandonment. They both would want to escape and make their realities different. However, it is Tom who takes the step and moves away trying to find himself, and some peace.
I didn't go to the moon, I went much further - for time is the longest distance between places.[...]
I left Saint Louis. I descended the step of this fire-escape for a last time and followed, from then on, in my father's footsteps, attempting to find in motion what was lost in space