On what grounds Islam is considered a better religion than any other religion? Please explain.
We Muslims do not claim that there are many religions created by humans for their benefit and Islam is the best amongst them. Instead, our claim is that God Himself responded to the need of religious guidance in man by sending the message of Islam. It was sent through many earlier messengers, including Moses and Jesus. Finally it was revived and presented in its pure form again for the last time through Muhammad, may God shower His blessings on all of them. Your question should therefore be this: How can it be shown that Islam is the religion sent by God for the humans?
There are basically two areas one should look for in trying to find out if the claim of Muslims about the divine origins of Islam is correct: authenticity of the claim that the process through which the message was communicated to the later generations was reliable and the ability of the contents of the message to convince that it is from God.
As for the authenticity of the message of Islam, we Muslims can show it confidently that its message as described in the Qur'an and preserved in the religious example of the Prophet (sws) is still exactly the same as it was during the Prophet's (sws) time. The Qur'anic text has been preserved through the process of memorizing done by hundreds and thousands of people in every generation while the Prophet's (sws) religious example was preserved through the unanimous practice of the Muslim community which was transmitted by an uninterrupted chain from one generation to another.
There are many ways one can adopt to investigate if Islam does present itself as God's religion. Perhaps the best way is to read the Qur'an for the purpose to find out whether its contents seem to originate from God or not. Of course, the most significant question a non-Muslim must seek to get answer to while reading the Qur'an is if the text seemed to be the Prophet's presentation or did it really appear to be God's own word.
There are four arguments which the Qur'an presents to show that it is indeed God's word: the impeccable character of the Prophet (sws), the highly convincing contents of the Qur'anic text, the prophecies in the earlier scriptures about the arrival of the Prophet (sws) coming true, and realizing of the prophecy made by the Qur'an that the Prophet (sws) and his companions would prevail and his enemies would perish. It is for the sincere seeker after truth to look into each one of these areas of understanding and find out for himself whether the Qur'an appears to him as the word of God or not.