Both queens were descendants of Henry VII and as such rivals for the English throne. They were kinswomen, but could not have been more different.
Mary the Queen of Scots, queen at birth, the much protected daughter of Mary de Guise, the pawn of her Guise uncles, the pampered and cosseted future Dauphine of Henry II, and playmate to the Dauphin.
Elizabeth should have been the direct heir of Henry VIII, but she never knew if she was the heir or bastard, it all depended on whether her father Henry was in a good mood. Throughout her life, Elizabeth was insecure, sometimes feared for her life. She was slighted, tormented by the fate of her mother Ann Boleyn.
The two queens could not have had a more different upbringing.
Sadly for Mary her life at the Court of France was her undoing, her ruination. She never learnt how to shoulder responsibility, how to plan, how to exercise control, all the makings of a queen. But did anybody expect her to rule? No of course not, that would be the task of her powerful uncles the de Guises.
Elizabeth however with no one to pamper her, no one to cosset her, did what she could in her very limited and constrained life, she studied, she learnt new languages, she learnt to plan but most all she learnt to be calm, exercise extreme self discipline and control to the point of eschewing all personal desires.
That was one of the reasons she never married, for she believed she was the Virgin Queen married to England and her subjects believed in her implicitly, that was one of the reasons her Kingdom had such peace and prosperity. On the other hand Elizabeth was ruthless, any claim to the throne was dealt with severity, so many noblemen with very tenuous claims to the throne were imprisoned in the Tower for years.
After the death of her first husband King Francis II, Mary returned to Scotland but she was unhappy there, it was cold and the noblemen did not much care for the frivolity of the French Court, that was when everything started disintegrating for Mary.
Although Elizabeth promised to meet Mary she just vacillated, to some extent these delays and the impressions one had of the other from the various emissaries exacerbated the gulf between them. Mary was beautiful, extremely charming, everybody loved her but she was terribly lonely and lacking Elizabeth’s fortitude believed that to govern her country Scotland, she needed a husband to help her or do it himself, much like her uncles would have done.
This is when Elizabeth failed Mary completely, she just refused to grant her permission to marry, Mary getting more and more desperate, lacking the strength and fortitude, ended up with two disastrous marriages and her subsequent flight to England seeking asylum. This plunged Elizabeth into a precarious position if not an extremely dangerous one.
Could she have saved Mary? Maybe, but most possibly not. There were so many extenuating circumstances; her councillors were of the opinion that Mary should be beheaded immediately to save England. And so it was done