Has the Catholic Church made any comparative study of the faith of Martha vis-a-vis that of Mary? At Luke 10:40-42 we read : " But Martha was distracted with much serving; and she went to him and said, “Lord, do you not care that my sister has left me to serve alone? Tell her then to help me.” But the Lord answered her, “Martha, Martha, you are anxious and troubled about many things;  one thing is needful. Mary has chosen the good portion, which shall not be taken away from her.”

But, at John 11:20, we see Martha taking the lead role in the events which  lead to the resuscitation of Lazarus by Jesus : " When Martha heard that Jesus was coming, she went and met him, while Mary sat in the house "

My question is: Has the Catholic Church made any comparative study of the faith of Martha vis-a-vis that of her sister, Mary, though the words of Jesus at Luke 10: 42 would have one believe that Mary was better  at expressing her faith?
Catholic theologians have compared Martha and Mary. The distinction they make is between the active life (of Martha) and the contemplative life (of Mary), not between their degrees of faith.

For example, St. Thomas Aquinas has a question on the active life in comparison with the contemplative life in his Summa Theologica II-II q. 182, where he mentions Martha and Mary frequently.

Addressing "Whether the active life is more excellent than the contemplative?" (a. 1 c.), he says:


  …the contemplative life is simply more excellent than the active.


He mentions several reasons, some of which are:


  
  because the contemplative life is more delightful than the active; wherefore Augustine says (De Verb. Dom. Serm. ciii) that "Martha was troubled, but Mary feasted."
  


&amp;


  
  because in the contemplative life man is more self-sufficient, since he needs fewer things for that purpose; wherefore it was said (Lk. 10:41): "Martha, Martha, thou art careful and art troubled about many things."
  


&amp;


  
  because the contemplative life is according to Divine things, whereas active life is according to human things; wherefore Augustine says (De Verb. Dom. Serm. civ): "'In the beginning was the Word': to Him was Mary hearkening: 'The Word was made flesh': Him was Martha serving." 
  


In a. 2 he shows that the contemplative life of Mary is more meritorious than the active life of Martha because (ibid. c.):


  the root of merit is charity; and, while…charity consists in the love of God and our neighbor, the love of God is by itself more meritorious than the love of our neighbor


So, although Martha and Mary might have the same degree of faith in God, the contemplative life of Mary is superior to and more meritorious than the active life of Martha (cf. Lk. 10:42: "…Mary hath chosen the best part.…"). Mary is not divided (cf. 1 Cor. 7:33) between God and the world, but can devote herself 100% to God.

An excellent work on the relationship between the active and the interior/contemplative lives, the necessity of the latter for the former, etc., is:


The Soul of the Apostolate by Dom Jean-Baptiste Chautard


Fr. Réginald Garrigou-Lagrange, O.P. discusses the necessity of contemplation for all Christians, because the "infused contemplation of the mysteries of faith and the union with God which results therefrom" is "in the normal way of sanctity" (i.e., everyone must pass through this way to become a saint / go to heaven). Cf. his works:


The Three Ages of the Interior Life: Prelude of Eternal Life


and


Christian Perfection &amp; Contemplation