The most likely place to find a difference would be in the quantum realm. We've studied the equivalence of gravitational mass and inertial mass on the large scale for quite some time. We've looked at stars, black holes, and all sorts of large scale things. We find them to be the same at these scales. While we can't really talk about liklihood of discovering "new physics," its unlikely that we'll find it where we have looked before.
At the small scale, however, there's room for question. It is extraordinarily difficult to measure gravitational effects on the small scale because the effect of gravity is so small compared to the other forces at play. As such, it is hard to claim we have strong evidence of gravitation behaving the same on these scales.
We are yet to observe any discernible difference at this scale, but the field is more wide open for future exploration due to the raw difficulty of making reliable measurements of gravity on this scale. Technological advancements could expose new data to answer this question once and for all, or we may just keep peering at smaller and smaller things without seeing any changes.