The hybrid power is still a big issue for the private teams to overcome, as well as the fact that they've had to run on Toyota spec tires pending Michelin developing privateer spec tires.
Possibly, they can match Toyota for speed on a clear track, but the added power and torque of Toyota's hybrid system is probably difficult to overcome. Especially if EOT/BOP is still off. However, on that end at Shanghai, I do feel that they're headed in the right direction there.
If the private teams get their new tires and EOT/BOP is good, I still think that Toyota will dominate the final results, as you'd expect a factory team to. But if the privateers can make a race of it, at least for a while, that's probably the best we can ask for. And if we get that, this is how I'll feel about it (gratuitous Victoria Justice gif incoming):
