Short answer: the solar system would be less stable in the short run due to the massive gravitational influence of Jupiter vanishing.
Long answer: The current layout of the solar system is actually remarkably well balanced; without outside interference, it'll stay stable for a good long while. Anything that changes the current equilibrium will force the system to adjust until it finds a new equilibrium. Removing a huge mass will certainly affect this in some way, but it's difficult to say exactly how without running a few hundred simulations. Jupiter's gravitational influence kept the asteroid belt from coalescing into a planet, so that might happen, for one.