Sorry, I didn't correctly state the question. I actually meant in Orbiter itself. You can change that in the Extra tab -> Time propagation -> dynamic state propagators.
By default it uses RK methods of differing orders (RK2, RK4, RK6, RK8)
Higher order propagators are almost always more accurate, but they will sacrifice some performance (mostly unnoticeable with a few vessels and Orbiter's zonal gravity). In a case where the higher order models were impacting performance so much that you were getting like 1-5 fps, you're probably loosing accuracy in that case.
There is a document in the doc/technotes folder that discussed accuracy. From my memory, the default propagator settings are still good enough that other things (ephemerides, atmosphere, gravity model, roundoff) will probably contribute to error quicker than the propagator itself will. Unless you care about centemeter accuracy over thousands of orbits, you probably don't need to change them.
On the other hand, Orbiter is a simulator, and discovering how a difference in propagators effects accuracy is definitely something you can do yourself, if you want to set up some test cases, and compare results. Run it like an experiment, with he default as a control.
The symplectic integrators are a little different than the Runge-Kutta. They sacrifice a little bit of positional accuracy, but because they're based on Hamiltonian mechanics, they guarantee conservation of energy. It just depends on which is more important in your test case.