All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.
The best and most beloved names to Allah are those that include being enslaved to Allah (Abd + One of the Names of Allah) as mentioned in the authentic hadeeth that says that the Prophet said, “The most beloved names to Allah are ‘Abdullah and Abdur-Rahmaan.” [Al-Bukhari and others]
Therefore, the best of the two names that you mentioned are Abdullah only, or Abdul Muqeet only. The name that we choose for your son is Abdullah [without being added to any other name].
As regards the name Muqeet Abdullah, it is a problematic name, so we do not recommend that you name your son with it.
Allah knows best.