When you use different solvers, even if in theory they converge to the same point, in practice the different algorithmic flows, different step sizes, and so on, will result in differences in round-off. If your system is unstable those differences in round-off can get magnified greatly (I think one of the Simulink examples specifically shows an unstable system for illustration.)
Even if the system is stable, if the algorithms are not coded exactly the same way, you will get round-off error. This is inescapable in any finite mathematical system, no matter what precision you use.
