There are many ways to Pray, some may Pray in thanks, others for well being, but one of the most talked about is Praying for Forgiveness of our Sins. First it is important to establish what the basics of a prayer and how it should be done.
Matthew says it best in (6:5-8) “And when you pray, do not be like the hypocrites, for they love to pray standing in the synagogues and on the street corners to be seen by men. I tell you the truth, they have received their reward in full. 6But when you pray, go into your room, close the door and pray to your Father, who is unseen. Then your Father, who sees what is done in secret, will reward you. 7And when you pray, do not keep on babbling like pagans, for they think they will be heard because of their many words. 8Do not be like them, for your Father knows what you need before you ask him.
To Forgive is essentially to cease to feel resentment against. Forgiving is something done by one who was wronged by another. If I slapped you, you would have to be the one to forgive. I could beg and plead your forgiveness, but you don't have to give it. When we do something wrong to another, we don't ask someone else to forgive us, that would be like if I slapped the waitress at the diner, and asked you to forgive me for her.
To have Remorse is to have a gnawing distress arising from a sense of guilt for past wrongs. Unlike Forgiving, feeling remorse, is a self act, requiring no one else. It is a feeling that comes from within. If I have slapped you then I should feel badly about it.
The Bible says we should Repent our sins, To Repent is to feel regret or contrition. In the biblical sense to turn from sin and dedicate oneself to the amendment of one's life. What this really means is to truly feel sorry for ones actions to be remorseful and make an effort to change. To repent is an act of the self, not the act of another.
So when we Repent our sins, it means we need to change that part of our life that caused the sin. If we just pray for forgiveness, we make no effort.
So is it better to Pray for forgiveness, or to acknowledge our sin to God? If we look at the passage from Matthew, “For the Father knows what we need before we ask him.” and “do not keep on babbling.” God knows our inner most intentions, If we need forgiveness he knows, if we feel regret he knows, if we wish to change, again he knows. So in prayer, it is probably best to just acknowledge our sin, rather than to draw out a lengthy monologue that God is already aware of. But we probably shouldn't acknowledge or ask if we aren't going to attempt to change, if we don't truly feel bad for our actions. That would be like playing catch without a ball, it doesn't work very well.