Do the "schwarzschild metric" or the "isotropic metric" fit the Event Horizon telescope data on Messier 87 better?
One of the things that can be confusing for beginners to GR is that there is no physical significance to the choice of coordinates we make. For example when studying static black holes we can use Schwarzschild coordinates, isotropic coordinates, Gullstrand-Painlevé coordinates, Eddington-Finkelstein coordinates, Kruskal-Szekeres coordinates and lots of others that I can't think of offhand.

But regardless of what coordinates we choose it's the same metric, just written in different ways. You ask about the Schwarzschild metric and the isotropic metric as if they were different things, but it's the same metric just written in different coordinates. It would be better to call them the static black hole metric written in Schwarzschild coordinates and the static black hole metric written in isotropic coordinates but, well, life is too short and even experienced physicists will just say Schwarzschild metric and isotropic metric to save time.

The point is that the coordinates are not directly observable. We choose some coordinate system and then do a calculation to compute something that is observable e.g. the trajectories of photons. And the results will come out the same. After all the photons don't care what coordinate system a physicist chooses to compute their paths.

The reason we have all these different coordinates is that it's often the case that some calculations are easier in some coordinates than others. For example the Schwarzschild coordinates are the closest to our intuitive grasp of the geometry around the black hole. If we were considering simple questions like the time dilation for an observer hovering near the black hole I'd use Schwarzschild coordinates to do this because they make the calculation easy. But Schwarzschild coordinates don't work well at the event horizon. If I was explaining why light can't escape from a black hole I'd use Gullstrand-Painlevé coordinates.

To return to your question, I'm not familiar with the method the JPL team use for computing trajectories in the Solar System so I can't comment on why the calculations would be easier in the isotropic coordinates than in the Schwarzschild coordinates. Presumably the computational method they use is easier in isotropic coordinates, but the observables that they calculate will come out the same regardless of which coordinates are used.

In any case neither coordinates are useful for the EHT calculations because Messier 87* is rotating not static and the spacetime geometry around it is described by the Kerr metric not the Schwarzschild metric. The Kerr metric can also be written in lots of different coordinate systems - I don't know which coordinate system the EHT team used.