Hazrat Maryam (RA) And Hazrat Fatima (RA)

 
Allah(swt) says in Qur'an:

"O Marium! surely Allah has chosen you and purified you and chosen you above the women of the world."
[3:42]
Does this ayah proves that Maryam (RA) has greater Status than Sayeda Fatima Zehra (RA) ?
I would like to highlight some points:

وَإِذْ قَالَتِ الْمَلَائِكَةُ يَا مَرْيَمُ إِنَّ اللَّـهَ اصْطَفَاكِ وَطَهَّرَكِ وَاصْطَفَاكِ عَلَىٰ نِسَاءِ الْعَالَمِينَ

O Marium! surely Allah has chosen you and purified you and chosen you above the women of the world
[3:42]

So, Allah has Chosen Hazrat Mariyam above all the women of the World and not whole universe.

2nd, we know what Holy Qur'an says about Holy Prophet;
[53.3] Nor does he (Muhammed) speak out of desire.
[53.4] It is nothing but revelation that is revealed,

The gist of above Ayaats is "Holy Prophet speaks nothing but what is revealed to him" and then we see following Hadith quoted by Most Sahih Sunni books references are provided below, which says Faima is the head of the women of Paradise, who is leading Hazrat Maryam (RA) in the heaven and here-after? according to sahih hadith, it is no one but Hazrat fatima (RA) Heading women of Heaven including Hazrat Maryam (RA) .

The Prophet (pbuh) said, "Fatima is the head of the women of Paradise."
Sahih Al-Bukhari, v. 3, Kitab Al-Fadha'il, Chapter on the Virtues of Fatima, p. 1374; Mustadrak Al-Sahihain, v. 3, Chapter on the Virtues of Fatima, p. 164; Sunan Al-Tirmidhi, v. 3, p. 266; Kenz Al-Omal, v. 13, p. 193; Muntakhab Kenz Al-Omal, v. 5, p. 97; Al-Jami^ Al-Sagheer, v. 2, no. 564, p. 5760; Seir Alam Al-Nubala’, v. 2, p. 123; Al-Sawaiq Al-Muhariqa, p. 187 & 191; Khasai’s Al-Imam Ali of Nisa’i, p. 118; Yanabi^ Al-Mawadda, v. 2, p. 79; Al-Jawhera Fi Nasab Ali Wa Aalihi, p. 17; Al-Bidaya wa Al-Nihaya, v. 2, p. 60.


So, its Proves that status of Sayed Fatima (RA) is greater than Holy Mary (RA) But they were both Masoom.