Completely different design can be related to graphical updates, when you have to conserve space because you don't want PCs to start melting so you re-use models. They have more space now, so they can put in more stuff, so they made it unique-looking. Pretty cut-and-dried to me.

not take-able
wasnt able to be removed in bloodmoon, it was just an activation key and was a piece of the environement
same case here
taking it would be like trying to take a cave wall or draugr sarcophagus ingame and leave with it
it just isnt meant to be taken

It is a magical enchanted axe that cannot be removed and the ghost of Hrothmund speaks to those who touches it, if he deemed those worthy enough. There is NO WAY of obtaining... Especially without ticking off a dead guy that can easily be all up in ye' head.

Ha!

I didn't play any of the TES games before Oblivion, so I didn't have the background story of Bloodmoon floating around in my cranium. I suppose it makes sense, based on some comments above, that the axe should still be un-take-able.

Maybe somebody did find a way to pick up the old axe and left their old axe in it's place just to mess with us.

Old dead guy who owned the original would be a bit pissed and probably wouldn't want to talk to those who touch the new axe. Or he'd send them on a quest to go get it to prove they are worthy.