Tom and his wife really don't share much of anything besides their miserly ways and their dislike of each other.
Tom's wife isn't afforded as much detail in her characterization as Tom is, but she is repeatedly said to be just as miserly as he is, if not moreso. Specifically, she tends to hide things that should be "common property", which leads to many of their fights. She is loud and unreserved in her criticisms of Tom, and Tom in turn appears to be equally short-tempered with her, to the point of striking her in the face on more than one occasion.
Their similarities are most evident when Tom returns home with the news of having met Old Scratch and negotiated a bargain with him for the old treasure. Tom might have gone along with the plan if his wife had not been so eager for him to do so; instead, he becomes reluctant for no other purpose than to infuriate her. Thus both characters seem to be primarily motivated by antagonizing the other, to the point that they spite themselves in the process.
There are a few other minor details, such as the fact that neither Tom nor his wife appear to have a job or friends, and they are well known for their poor tempers and behaviors.