aborted take-offs in the sim and those for real are (from my experience) very close. Our company send us to Flight Safety for sim training, and they do have very good sims out there though.
Generally most things are pretty close, but there are some areas where it's noticeablly different. eg in the aircraft I can really notice any slight changes in G when I'm hand flying, but not so much in the sim. The sim is also more sensitive in pitch than the aircraft. Turbulence is a strange one as they can make it pretty rough in the box, but it's "different" to the real thing, I guess it's more random in the real world if that makes sense.
Smoke in the cockpit is not simulated so when that occurs it's exactly as you would get in the real thing
. The drills are different though, in the sim it's get out (via the rope ladder if the airbridge is still up), sadly you can't do that in the aircraft.
Members of the public can hire sim time at European Skybus in Bournemouth, they used to have Boeing 747 and 737 for you to go and have a play. Actually it's not so much of a play, as they will actually instruct you in there so you get to do some "real tasks" which in my opinion is much more constructive and fun.