In the DMG there is an optional initiative rule called speed factor. It lists a bunch of modifiers for different weapon types and situations that affect your initiative roll. There's more to it than that, but that's not important for my purpose here. Anyway, the table lists a -2 penalty for two-handed melee weapons. That's completely wrong.
Now, I'm not an expert in medieval weaponry. I have, however, been taking medieval combat classes for a little while. I guess I can really only comment on the sword, as the class hasn't included things like axes or spears, but it has been clearly demonstrated by the instructor that the longsword is noticeably faster when used with two hands rather than just one. Now, I'm not talking some giant monster two-handed sword that you couldn't possibly use one-handed. Though looking at that table, it also gives a penalty for a heavy weapon, so if I were to use speed factor, I would consider just ditching the two-hander penalty and only apply the heavy weapon penalty.
It basically has to do with greater control of the sword. To really hit someone hard with a one-handed weapon, you pretty much have to get some momentum behind it. When you have two hands on the hilt, it takes a lot less motion to get power behind the hit. Does this apply for the other versatile weapons besides the longsword? I'm not sure, as I haven't worked with an axe or spear. Honestly, I would assume so if I was using speed factor and I'd just dump that two-handed penalty altogether.
Just my .02.