What law does Mayella break? What social code does she violate? Which would most citizens of Maycomb consider the more serious crime and why?

I think it is important to consider that a little more is going on than just lying under oath vs. a black man in contact with a white woman.

#1: She lies under oath because it is actually her father who is guilty here.  Obviously we can't know if she does this to protect him or because she fears him.  A little of both?  This is almost forgivable by today's standards.

#2: She is not simply a white woman in contact with a black man.  She makes sexual advances on Tom.  She, in fact, kisses him.  This is what is so shameful.  And she does it because she is so lonely, dejected, insecure (something), that this is the only man she can get attention from.  To Maycomb - it is shameful because he is a black man.  But it it might also be considered shameful today because he is married.

Even by today's standards it is easy to see which "crime" would be considered more serious.