An unmuffled, or dampened, drum will 'ring' for quite a while... depending on the acoustics of the room. Looking beyond 'tone' for a moment, (because dampeners also effect the tone), I have played in rooms where because of the acoustics of the room itself the 'ring' was not a factor. That's extremely rare, however.
If it's possible to express this in words.. unmuffled you get "Booooooinnnnnnnnnnnnnggggggggggggg" where as muffled you get "THUMP".
If you asked me for the one thing that miff's me about drums the most I wouldn't have to think twice - it's this: The sound out front compared to the sound behind the kit, (on the drummers stool), are so radically different that there really is no comparison. Again, this is very dependent on room acoustics... but I have played in rooms in which the sound I'm hearing from behind the kit sucks... but the sound out front is quite good. I hate this to no end - because It really has an impact on how well I'm playing, and what I'm playing. It's one of several reasons some drummers wear headphones... or some alternate form of hearing their kit.
I do not like playing electronics as much as acoustics BUT... it is GREAT to hear from the drum stool what the people in front of the kit are hearing, (in this case thru the mains, of course). Also the ease of setup is nice for old guys like me.