- Κύριε Ἰησοῦ Χριστέ, Υἱὲ τοῦ Θεοῦ, ἐλέησόν με τὸν ἁμαρτωλόν. /Greek/ (The 'ἁμαρτωλόν' word is optional.)
- Lord Jesus Christ, Son of God, have mercy on me, the sinner. (The 'sinner' word is optional.)
- Hare Yeshu Hare Yeshu Yeshu Yeshu Hare Hare Hare Christa Hare Christa Christa Christa Hare Hare /sanskrit with English transliteration/
- Hare Krishna Hare Krishna Krishna Krishna Hare Hare Hare Rama Hare Rama Rama Rama Hare Hare /sanskrit with English transliteration/
The mantras above are the same. The first two are the Jesus prayers (https://en.wikipedia.org/?title=Jesus_Prayer), the last one is the Maha mantra and the third one is the Jesus prayer in sanskrit. They are the same, no difference.
In these prayers or mantras:
Rama is the name of the incarnation of Vishnu (God) in the Treta yug
Krishna is the name of the incarnation of Vishnu (God) in the Dwaper yug.
Yeshu Christa or Jesus Christ is the name of the incarnation of Vishnu (God) in the Kali yug.
The word 'Hare' has come from 'Haran' which means to take way or to end. So when one says hare Yeshu/Christa/Krishna/Rama, he requests the God (the supreme consciousness) to take away his sorrows, his shortcomings, his failures and pains.
So 'Hare' and 'have mercy on me' means the same. The other Words are the words of the Name of God.
"harer nama harer nama harer namaiva kevalam
kalau nasty eva nasti eva nasti eva gatir anyatha"
- A Sanskrit verse from Brhan-naradiya Purana
which means:
"In this age of Kali, there is no alternative, there is no alternative, there is no alternative for spiritual progress other than the chanting of the holy name, the chanting of the holy name, the chanting of the holy name of the Lord."
So in Kali yug, there is no way for Self realization, neither karma yoga, nor hatha yoga, nor raja yoga, nor dhyana yoga, nor jnana yoga, none of them leads to Self realization except of bhakti yoga and repeating the Name inside.
The mantra of the Name is a very easy mantra. You can chant it anytime, anywhere. Give at least 15 minutes per day for this mantra repetition. Sit quietly in a comfortable position. Then either chant it silently or loudly. Repeat it with full awareness of its meaning which is " O Lord, take away all my sorrows, pains and shortcomings and give me bliss and joy".
Source: http://www.meditationiseasy.com/mCorner/techniques/Hare_Krishna_Mantra.htm