So defensively, the Player has type 8/9 immortality, limited teleportation, precognition, time-paradox immunity, and exists non-corporeally. While ST has type 8 immortality, immunity to time manip, and high-godly regen.
Offensively, player has causality manip, probability manip, BFR (doubt it will work on this nigh-omnipresent), death manip, spatial manip, and existence erasure. However, I don't think any of that would let the player get around high-godly regen.
On the other hand, ST has matter manip, soul manip, and duplication. Even though I'm not very familiar with DC, I think ST should be able to steal the player's soul without too much trouble, the wild card being the player's type 8/9 immortality.
Tentative vote for Swamp Thing. If the Player's type 8/9 immortality is strong enough to persist through soul stealing + matter manip, then I'd switch to inconclusive.