Should I repeat after the muezzin or pray Tahiyyat al-masjid?

It is better for you to repeat after the muezzin and then
pray Tahiyyat al-masjid, so that you will have done two acts of worship
together, namely repeating after the muezzin then praying Tahiyyat
al-masjid.  

But if that is on a Friday then it is better to hasten to
pray Tahiyyat al-masjid, so that you can them focus on listening to the
khutbah, because listening to the khutbah is more important that repeating
after the muezzin. 

Shaykh Ibn ‘Uthaymeen was asked: If I enter the mosque and
the muezzin is giving the call to prayer, is it better to pray tahiyyat
al-masjid or to repeat after the muezzin?

 He replied: 

That depends. If you enter when the muezzin is giving the
call for Jumu’ah prayer, the adhaan that is given when the khateeb is on the
minbar, in this case we say that you should hasten to pray Tahiyyat
al-masjid, and you should not wait until the muezzin has finished, because
preparing yourself to listen to the khutbah is more important than repeating
after the muezzin, as listening to the khutbah is obligatory and responding
to the muezzin is not obligatory. 

But if the adhaan is not for Jumu’ah prayer, then it is
better for you to remain standing until you have responded to the muezzin,
and offered the well-known du’aa’ after the adhaan:  

Allaahummah Rabba haadhihi’l-da’wat il-taammah wa’l-salaat
il-qaa’imah, aati Muhammadan al-waseelata wa’l-fadeelah, wab’athhu maqaaman
mahmoodan alladhi wa’adtahu innaka laa tukhlif
al-‘mee’aad (O Allaah, Lord of this perfect Call and the Prayer to be
offered, grant Muhammad the privilege and also the eminence, and resurrect
him to the praised position that You have promised, verily You do not break
Your promise), 

Then after that you can pray Tahiyyat al-masjid.  

Fataawa Ibn ‘Uthaymeen, 14/295.