Well first of all, the helis in the sim fly based on a 'perfect' mechanical set-up. Most people when first starting out (myself included) rarely have their heli set up perfect due to lack of experience, so your real one likely won't be as stable.
Also the larger the heli the more stable it will be so it is best to practice with a model that is the same size as the one you fly or plan to buy.
And as mentioned above you tend to be more relaxed when flying the sim since a push of a button after a crash and you are set to go but will be more tense when flying the real thing. Of course since you instruct new fixed wing pilots you probably see how nervous they can get when learning to fly the real thing. ( Generally referred to as the 'pucker factor')