I have a theory. The premise isn’t mine, but I forget who I first heard mention it. What if the Crucifixion were an elaborate ritual to kill a particularly powerful Immortal (ie the mortal avatar of the White God), or perhaps to dislodge his mantle so it could be transferred?
Based on the power level of the artifacts these days, it seems reasonable that Big Juju was going down during the Crucifixion. Based on the relative power of the shroud in DM vs the shroud in SG, its likely much more than just the accumulated faith of today. Based on the historic view that the Old Testament Christian God and the New Testament seem to have different personalities/characterizations, it would fit that that the Crucifixion were the event responsible.
So, assuming for the sake of argument that that's indeed what was happening, what role might each of the artifacts played? And for the record, I dont know when or how the items got Power, whether the items were empowered ahead of time or empowered by the events themselves. The revealed original names of the Swords implies that they managed to call existing Power to those particular objects (a sort of Object-mantle, for lack of a better term), so it's possible that these object had similar manifestations in other cultures.
We have a total of 8/10/40 artifacts associated with that field, and by ones we know the most about is, by far, the Swords. (For this theory Im assuming the knife is indeed the Spear). These are all part of the
https://en.wikipedia.org/wiki/Arma_Christi- Three Swords
-Fidelacchius/Kusanagi
-Esperacchius/Durendal
-Amoracchius /Excaliber
- Grail
- Knife/Spear
- Crown
- Shroud
- Placard
- 30 Coins
- Noose
The Swords = Restraint: These have the stated purpose of restraining all supernatural advantages of the Knight's enemy, forcing them to play by the Mortal rules. The Nails were used to restrain the body of Christ, locking him to the Cross
Grail = Purification: The Grail is generally as an artifact of Purity and Healing, and was used ahead of time during the Last Supper. It would follow that the Cup was used as part of a Pre-crusafixion-ritual purification, similar to what Harry does before major rituals. However, since it received the Blood of Christ ahead of time, it might have played some kind of thaumaturgical role, and "some traditions do say Joseph of Arimathea used to catch his blood at the crucifixion"(Wikipedia).
Crown = Responsibility: In the abstract this is what declared him to be the King of Jews, which per the Sword's royalty requirement is an important metaphysical attribute. However, the placard does this similarly, and there were several Mock-royalty items involved (a reed for a scepter, purple Robe, etc). It would appeal to me if the Crown of Thorns was actually the original prototype of the Thorned Manacles, and so had similar powers.
Placard = Name: This (in the abstract) shows and represents the Name of Christ, which would be all kinds of important for most any such ritual. It also anchors him as the King of Israel/The Jews, which per the Sword's royalty requirement is an important metaphysical attribute. Its powers will be Name related somehow; either reveal a TrueName, or perhaps forcibly Change it.
Shroud = Preservation: It's supposed to have healing powers, so I’m guessing that this is responsible for sustaining Jesus's Body while he was off on a Soul-walkabout (to Purgatory by some traditions), essentially like what DR and Mab did for Harry.
Knife/Spear = Death (Change): This is what did the deed, so to speak. The logical assumption on primary power is to Kill Anyone, Kill Immortals, Forcibly sever/remove a Mantle from its current Host, or similar. This could then be why it gained the reputation of ensuring Victory.
30 Coins = Choice: The Coins represent the Mortal's Freedom to Choose Evil. The Coins gain the Power to Increase the Freedom of the disgraced Fallen by allowing them to tap that same mortal Right to Choose Evil. Since the Swords arguably Impede Freedom, and the promotion of Freedom is the stated definition of Good in the DV, such Restraint would be fundamentally counter to the MO of the Heavenly Host, which is why the Coins gain a balancing Power.
The Noose = Retribution: This is the representation of Judgement, and the inescapable consequences of mortal Choice. It grants access to a Curse, symbolic of the Jew's Choice to free Barnabas rather than Jesus, and Im thinking a more poetic expression the idea of the Inescapability the Death that one is Fated for (in that case the Noose itself).
(Edited to correct typo's that haunt me. -Quantus)