Okay, just cuz going to go through all of these.
Tamano -Elemental Manipulation, Not going to help, tifas counters her and vice versa
-Poison Manipulation, Assuming Tifa has all of her materia, she cures herself so this wont help.
-Shapeshifting, wont work in a fight
-Summoning, Generally as useful as hers, but she has more 'power', going to lean to her on this one.
-Soul Manipulation, Probably the only hax she has that can hurt/kill tifa atm
-Magic Resistance Bypass, Tifa was always more powerful with her fists in other canon, so this wont be too helpful.
-Resistance to Curse/Matter Manipulation, I guess icing on the cake?
-Probability Manipulation, Forgot the context of this ability but Tifa has this with so many spells so I will just ignore this.
-Time Manipulation, As Per Gargolye said, Tifa can resist time manipulation with certain combination of materia etc so I will leave this be.
-Reality Warping, Scratch the above, this and soul hax is the only thing that can hurt tifa as far as I can see.
-Casuality Manipulation. I dont remember this being combat viable, so someone will have to correct me. Even so, Tifa can just use autolife on herself or her protective spells, should be okay.
- Life/Death Manipulation. Tifa survives auto life
-Fate Manipulation, a little hard for me to say conclusively. Could help with warping and soul hax, but I dont think it is how she will kill tifa.
-Power Nullification, Assuming I did all this work for nothing ggez tamamo wins, but also assuming this only works on active abilities, then Tifa should probably be okay.
-Mind Hax, Again, a means to an end, not a concrete way for victory.
-Spatial Manipulation, Helps counter tifa's aggressive fighting style in many ways? I guess that counts for something.
-Conceptual Manipulation, Going to not go down this rabbit hole.
Allright Tifa-
...basically just the same as above but she has no soul, concept, mind or fate hax.
To be frank, I dont know that much about fate, but even giving the skeptic route of half the above abilities Tifa has no way to kill Tamano, and Tamano can just obliterate Tifa before she can regenerate or hax to death.
Im going Tamano mid diff, only on the soul grounds that tifa will have a very hard time killing her, if not impossible time where as Tamano has so many ways to kill her.