My personal preference is for "trespasses", since it is what I first learned, and, in my experience, is the translation used by most Christians in America (at least the ones I've encountered). It flows better, and it's good to be able to pray at least the Lord's Prayer with other Christians who might not share our Orthodox faith.
With that said, I should say something in support of "debts", which is what we use in our English translations in church, along with "the Evil One" instead of "evil". What follows made its first appearance at youretc.com, but because it was not "Magisterium-loyal-Papally-Promulgated", it probably helped to get me banned.
In Syriac, the language in which Jesus would've spoken, the Lord's Prayer goes like this: Abun d-bashmayo
aykano d-bashmayo oph baro
hab lan lahmo d-sunqonan yowmono
washbuq lan hawbayn wahtohayn
aykano doph hnan shbaqan l-hayobayn
lo talan l-nesyuno
elo paso lan men bisho
metul d-dylokh hi malkutho
The phrase that is of concern to us in this discussion is washbuq lan hawbayn wahtohayn aykano doph hnan shbaqan l-hayobayn
. When this is literally translated, what we have is "forgive us our debts, as we have also forgiven our debtors
". This differs from "forgive us our trespasses, as we forgive those who trespass against us". The latter seems to ask God to forgive us in the same measure with which we forgive others. The former, Syriac version says something different; it asks God to forgive us just as we have already
forgiven those who sinned against us. It presumes that, before daring to call upon God for forgiveness, we have already done our part in forgiving others. When you think about it, this makes sense since, in the Gospel, Our Lord admonished us that if we are going to offer something to God, and then we remember that we have something against our brother, we are not to offer that gift, but rather set it aside, go to our brother and reconcile, and then only should we approach God with our oblation. It makes sense with Christ's teaching in the Gospel that before we ask for forgiveness, we should offer forgiveness to others.
And that's why Syriac is better than English.