Reasons for a simulated circuit to oscillate when the physical circuit does not
Your model of the solenoid is very simple- perhaps there is a lot of distributed capacitance across the coil. Try simulating that with some dozens of pF across the coil. Also, perhaps there is a cable between the circuit and the solenoid with even more parallel capacitance. 

Breadboards are not really great for this sort of thing, possibly you're getting some EMFs across the connections that are mucking things up (or stabilizing them!)- in particular I would suggest getting the high current paths off the breadboard (which probably means everything for such a simple circuit). 

It's possible the op-amp model is not perfect (typically they're macromodels and don't attempt to model the behavior exactly- in return for which you get an answer faster, even if it's not quite right). But I would expect this kind of application would be right in their wheelhouse.