As long as you physically break it in any way it should be enough unless someone really wants something from you.
The main reason you don't want to toss a full drive is that it's super easy to slot one of those into a dock and use it like an external drive and then reveal all the hidden files where you don't need the password that's normally used to log into a user ID on the machine. It takes less than 5 minutes and $20 dollars of equipment, which means any dumpster diver or retard who sees a PC sitting and ready to be picked up by trash collection can essentially have access to all of your computer if they so please if you don't destroy it. It's less about people finding out you say nigger on the Internet, and more about your bank account.