Nagato'll win mid difficulty, once the third Raikage gets into close range he can expect to have his chakra drained reletivly fast. Nagato can then either shinra tensei him away if he feels like the Raikage, with his lightning armor and his lightning coated fingers gone is still a big enough threat.
Or he could activate his Asura path and hold him down and then use the same technique he was planning to use on Bee, on the Third Raikage.
The animal path will be useless, for the most part. The only advantage the animals would give Nagato would be the combined sight, and possibly being able to fly and avoid the Third Raikage (If Nagato is threatened enough by him, though I doubt he is,).
And the Raikage would inflict some damage to Nagato, but I feel that confronting him in melee range would be the downfall of most ninja. And sadly the Third Raikage has been only fighting in melee range (I believe, has been awhile since I read his fight).