I think the problem of the fame system is it isn't very clear. It isn't design to give you any sense of accomplishment. It is there to tell you you did something and you gained points for those actions. I never understood Tom's idea of making people find out stuff to be honest especially regarding stuff like fame.
The achievement system is well known. It is clear on how to get the achievements and sometimes tells you how many managed to get the achievement. It is easier to understand and straightforward.
I can't really think of any advantages of the fame system which the achievement system does not have. The fame system just feels poor imitation(or less developed version) of the achievement system and should be replaced. It doesn't really add much to the game. You can't keep track of any of your deeds in the current fame system so you as a player has no idea what you did to earn those points. There are of course known points but if you haven't been tracking your actions, it is pretty hard to find out where you got your points.
