There were some general changes to Sponsored Magic made in the Paranet Papers in order to better reflect the books. Most telling is that they changed sponsored magic debt to be usable for basically anything. Extra shifts, fate points, to absorb consequences, it is really easy to get debt now.
In Paranet Papers the specifics of Soulfire as sponsored magic get laid out in more detail to match the books. So lets step through what they can do one bit at a time.
First we have partially satisfying the Catch
Sponsored: Treat the enemy as one level less potent in toughness abilities if they are opposed to your sponsor (summer/winter courts)
Soulfire: Counts at catch for any Holy or Divine weaknesses (not partial but fully satisfying catch). Always grants the one level less potent toughness abilites for ANY enemy (not just ones opposed to your "sponsor").
Second we have expanded abilities
Sponsored: Thaumaturgy at Evocation speed. Enhanced abilities (summers healing) without the knowledge checks.
Soulfire: +1 bonus to power or complexity on any thaumaturgy dealing with direct creation of something (illusion, veils, ward, items)
Third we have "supercharged" evocation
Sponsored: The big ticket here is that you can use your existing specializations and make them even better. You can combine theme effects: demonic patron + fire spell = hellfire
Soulfire: +1 bonus to power or complexity on any evocation dealing with direct creation of something. So "supercharged" fire might get +1 power if you are throwing up a wall of flame.
Fourth we have "sponsor debt"
Sponsored: You can use power from your sponsor at no immediate cost to you in a pinch but you incur a debt point to fill a gap. (Note this expanded to things not related to your sponsor now)
Soulfire: You don't have an external power source. While similar to sponsored magic in how it can be used you instead use the soul track. This line in PP is the key "The soul stress track replaces the sponsor for all practical intents and purposes"