One thing to note, though, is that if the two calculations match, then that's great and you can trust the results. But even if they don't agree, you still mig

One thing to note, though, is that if the two calculations match, then that's great and you can trust the results. But even if they don't agree, you still might be able to trust the results. Often these sorts of long-term simulations are only done in a statistical way. You can't trust the results of any individual simulation due to numerical uncertainties, but you can trust the aggregate results of a large set of simulations all run with slightly different initializations. (So, you could run many long term simulations of the Solar System to conclude that there is a 3% chance that Mercury will be ejected.)