Stone or iron mortar?
Stone is a much worse heat conductor than iron. It warms much slower from vigorous pounding than iron, and actually cools whatever is being ground. This is often desirable, as you don't want to warm whatever you are grinding - some spices contain fats which are viscous or solid at room temperature, but get liquid somewhat above it, so they would be seeping their aroma and converting to a paste if warmed while ground. 

Another argument for stone will be the smooth surface. Seasoned iron isn't as smooth as marble or granite can be polished, and if left unseasoned, you will need to remove rust from time to time (another problem of iron which harwig already pointed out), disturbing the surface. The mortar surface should be as smooth as possible. 

Also, the stone will require no maintenance apart from washing. Iron will have to be kept from rusting, so you'll have to season it. The grinding action will probably slowly eat away the seasoning layer, so you'll have to reapply it periodically, which is lots of work (well, the complete stripping first is what makes it lots of work, seasoning not so much). But if you use your mortar as seldom as I do, this shouldn't be a problem. 

On the other hand, iron's density is about 3 times higher than marble or granite, resulting in a much heavier pestle. While this means some more fatigue for you, it will result in a better grinding result. 

Another problem with stone is that it can crack if you happen to drop it on the floor. Luckily, a mortar is not easily dislodged from the counter, and granite breaks nowhere as easily as earthenware, but the chance exists. If you get stone, don't go for the tulip-on-a-stem shapes. While it may be convenient to grip the stem, it is also a weak point. 

You must also consider possible chemical reactions. Granite won't be a problem, but marble is acid sensitive. So making a pesto with lots of lemon juice is probably a bad idea in marble. It won't cause a comic-book like Chinese syndrome, but it will attack the surface, making it less smooth. Seasoned iron has some acid resistance, but strong acids are bad for it too.  

To me, the "tradition" argument isn't very strong. People have used abacuses for thousands of years, but I prefer a TI-42 simulator when I have to make a calculation too complicated for my brain. Both iron and stone will work. And as harwig says, aesthetics are individual - not that I need much of that in kitchen implements.