Answer
Short Answer: When a Muslim says Subhana Allah, he declares that his heart and mind are far removed from thinking that there is any shortcoming in Allah, or attributing any evil to Him, and declaring Him to be far above any fault that is attributed to Him. The simple and common meaning of Al-Hamdullilah is all praise and thanks belong to Allah the Almighty alone. Muslims say Al-Hamdullilah because Allah is the originator of everything, He is the Creator, the Giver, the Provider, the Sustainer, etc. The literal meaning of the word Allah is the only entity in existence Who truly possesses the qualities of divinity and lordship. The name Allah belongs only to Allah, no other one can be called Allah.
………….
Salam dear questioner,
Thank you for your question.
Best Type of Dhikr
Let me first confirm that the two phrases you are asking about are the frequently recited type of dhikr (remembrance of Allah) that Muslims say every day.
The Prophet (peace be upon him) said:
“Purity is half of faith. ‘Al-hamdu lillah (all praise and gratitude belong to Allah)’ fills the scales, and ‘subhan-Allah (how far is Allah from every imperfection) and ‘Al-hamdulillah (all praise and gratitude belong to Allah)’ fill that which is between heaven and earth.” (Muslim)
Meaning of Subhan Allah
With regard to the meaning of Subhan Allah, the word tasbih in Arabic includes many meanings such as negation, amazement, exaltation, majestic, etc.
Negation
The meaning of negation is reflected in these verses:
*{Allah has not taken any son, nor has there ever been with Him any deity. [If there had been], then each deity would have taken what it created, and some of them would have sought to overcome others. Exalted is Allah above what they describe [concerning Him]. }* (Quran 23:91)
*{And they have claimed between Him and the jinn a lineage, but the jinn have already known that they [who made such claims] will be brought to [punishment].
Exalted is Allah above what they describe.}* (Quran 37:158-159)
The word Subhana Allah negates what has been falsely attributed to Allah in terms of taking any son or taking any other deity beside Him.
Amazement
The meaning of amazement is reflected in this verse,
Exalted is He who created all pairs – from what the earth grows and from themselves and from that which they do not know. (Quran 36:36)
When a Muslim says Subhana Allah, he declares that his heart and mind are far removed from thinking that there is any shortcoming in Allah, or attributing any evil to Him, and declaring Him to be far above any fault that is attributed to Him.
Imam Ahmad reported that:
“When the Prophet came to a verse which spoke of Allah being above any fault or defect, he said Subhan Allah.”
Ibn Abbas is reported to have said:
“Subhan Allah means declaring Allah to be above every bad thing.”
There is no contradiction between the two meanings mentioned in your question. Therefore, it is not a matter of which meanings to be preferred over the other.
The Meaning of Al-Hamdullilah
The simple and common meaning of Al-Hamdullilah is all praise and thanks belong to Allah the Almighty alone. Muslims say Al-Hamdullilah because Allah is the originator of everything, He is the Creator, the Giver, the Provider, the Sustainer, etc.
Al-Hamdullilah is simply is translated as ‘Praise be to Allah’.
Al-Hamdullilah is an expression of gratitude to Allah for the things He gave, still gives and will continue to give.
Al-Hamdullilah is a combination of appreciation and thank.
Health Benefits of Dhikr
Scientists say that when we see something exciting, our adrenal cortex is stimulated. Followed by an increase in our blood sugar. This, in turn, stimulates the pancreas to secrete insulin into the blood to lower the sugar level, causing us to then feel tired or weak.
Based on this, we are recommended by the Prophet to say Al-Hamdullilah ” for what we have; and, “Subhana Allah” when we see something exciting or amazing.
The Opening Chapter of Al-Fatihah starts with the phrase of Al-hamdullilah. So every Muslim recites this phrase every single rak`ah (unit of prayer) that Muslims offer throughout the day which is a total of 17 times in obligatory prayer only.
Also after each prayer, the Prophet recommends that we recite Subhana Allah 33 times, Al-Hamdullilah 33 times, and Allahu Akbar 33 times.
The Prophet said:
“He who recites after every prayer: Subhan-Allah (Allah is free from imperfection) thirty-three times; Al-hamdu lillah (praise be to Allah) thirty-three times; Allahu Akbar (Allah is Greatest) thirty-three times; and completes the hundred with: La ilaha illallahu, wahdahu la sharika lahu, lahul-mulku wa lahul-hamdu, wa Huwa ‘ala kulli shai’in Qadir (there is no true god except Allah. He is One and He has no partner with Him. His is the sovereignty and His is the praise, and He is Omnipotent), will have all his sins pardoned even if they may be as large as the foam on the surface of the sea.” (Muslim)
The Meaning of the Word ‘Ilah’
The literal meaning of the word Allah is the only entity in existence Who truly possesses the qualities of divinity and lordship.
The name Allah belongs only to Allah, no other one can be called Allah.
The deeper meanings of the word Allah include the following:
Allah is the only One whom all creations praise and glorify.
Allah is the Provider, the Sustainer, the All-Knowing, the All-Hearing, the Ever Merciful and the Most Merciful.
Allah is the First before Him there was nothing.
Allah is the Last after Him there will be nothing.
Allah is the Manifest above Him there is nothing.
Allah is the Hidden below Him there is nothing.
Allah is the Only God on Him we put our trust.
Allah loves those who obey Him and promised them great rewards in the Hereafter.
I hope this helps.
Salam and please keep in touch.
Please continue feeding your curiosity, and find more info in the following links: