I like how in Morrowind and Oblivion the weapons are divided up like 'Blade, Blunt, Spear' etc, and I wish Skyrim was similar (instead of the 'One-handed, Two-handed deal). The thing is, if you pick up a two-handed sword - matter what type - you'll be swinging it like a big hammer, which it's not. A big problem with me was dreading seeing my Samurai in Skyrim swing his Dai-katana (it's Daedric, from Whiterun's Daedric quest) like a freaking warhammer. Fortunately, the Ebony Blade (tha daikatana) swings faster than the other 2H weapons.
But still, I got thinking. What if when leveling up you could choose:
-Faster attacks
-Higher damage
So your character would have the choice to be able to swing his weapons - including a greatsword - faster than what is average, however he would not get a damage bonus (aside from the natural bonuses you get). Otherwise, he could upgrade his damage, which would make the weapon swing slower, but with a lot more damage. In this way, you would get the sense your character is not only training in a type of weapon, but he's training to use that weapon in a specific way.
But only if you can choose one or the other. I don't like the idea of being able to choose Speed AND Damage, I want the players to really have to make the choice: do I want to be able to swing my weapon faster, or swing it harder? You can't choose both, you gotta make a choice!