Like I know Spice is more tool for university, while hspice and spectre are practically industry standards.
For a model bsim 3v3 hspice and spectre has different internal models(for example same parameter can have different values i.e. models could not be automatically translated ) , but simulated results should be the same. I think that spectre is generally faster and has less convergence problems, but theese differences should not ne significant.
If you need more accurate simulation, then you should make better mosfet model.
For example some big companies (for example infineon) have their own simulators
and more accurate models with more than 500 parameters for one mosfet.
For difference between spice and spectre you can read this book.