What is the difference between the Catholic version and the Lutheran version of the Lord’s Prayer?

Matthew 6

3 But when thou doest alms, let not thy left hand know what thy right hand doeth: 4 That thine alms may be in secret: and thy Father which seeth in secret himself shall reward thee openly. 5 And when thou prayest, thou shalt not be as the hypocrites are: for they love to pray standing in the synagogues and in the corners of the streets, that they may be seen of men. Verily I say unto you, They have their reward. 6 But thou, when thou prayest, enter into thy closet, and when thou hast shut thy door, pray to thy Father which is in secret; and thy Father which seeth in secret shall reward thee openly. 7 But when ye pray, use not vain repetitions, as the heathen do: for they think that they shall be heard for their much speaking. 8 Be not ye therefore like unto them: for your Father knoweth what things ye have need of, before ye ask him. 9 After this manner therefore pray ye: Our Father which art in heaven, Hallowed be thy name. 10 Thy kingdom come, Thy will be done in earth, as it is in heaven. 11 Give us this day our daily bread. 12 And forgive us our debts, as we forgive our debtors. 13 And lead us not into temptation, but deliver us from evil: For thine is the kingdom, and the power, and the glory, for ever. Amen.

Luke 11

2 And he said unto them, When ye pray, say, Our Father which art in heaven, Hallowed be thy name. Thy kingdom come. Thy will be done, as in heaven, so in earth. 3 Give us day by day our daily bread. 4 And forgive us our sins; for we also forgive every one that is indebted to us. And lead us not into temptation; but deliver us from evil.

Even in the same version of the Bible, the "authorized" (KJV) version, there is a difference!

Here is the Lord's Prayer as said by Missouri Synod Lutherans.

Our Father who are in heaven.
Hallowed be Thy name.
Thy kingdom come.
Thy will be done on earth as it is in heaven.
Give us this day our daily bread.
And forgive us our trespasses as we forgive those who trespass against us.
And lead us not into temptation.
But deliver us from evil.
For Thine is the kingdom and the power and the glory forever and ever. Amen.

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Here is the Lord's Prayer by Roman Catholics.

Our Father who are in heaven.
Hallowed be Thy name.
Thy kingdom come.
Thy will be done on earth as it is in heaven.
Give us this day our daily bread.
And forgive us our trespasses as we forgive those who trespass against us.
And lead us not into temptation.
But deliver us from evil.

http://www.spiritheart.org/chapel/lordpryr.htm#matthean

The 'difference' of which you enquire is known as the 'doxolgy'. It is a mistake however, to think that there are different versions of the Lord's Prayer for Catholics and protestants.

During the Catholic Mass those gathered pray the 'Our Father' up to the point of the doxology. The priest does then pray the doxology and those gathered respond with the final 'Amen'.

The two versions of the Lord's Prayer can be found in Mathew 6:9-13 and Luke 11:2-4.

With the exclusion of the doxology the petitions remain the same, ie, the content of the Our Father remains the same.

hope this helps!