Ok so I've played a bit of both classes, and like them both. They are very simaler in that they both have root/rot for soloing and heals and buffs. My question to you is what do you feel is the better class and why?

Better class for what exactly?

Shamans are great for buffing players and slowing
mobs. Matter of fact they have the best slow
spells, and the widest range of stat buffs.
Decent haste spells too.
They get the "cannibalize" line of spells
which swaps HP for Mana so that helps keep your
mana pool up.
They root and rot well (probably the best of all classes)
but cannot kite that I've ever seen. Shamans get a
pet spell at 35 and it upgrades as you go along.
Shamans are also the only class
that can do Alchemy (make potions)

Druids are the 2nd best healers in the game
(Clerics are the best) and they get nice HP and
resist buffs. They are the best Power Leveling
class too in my opinion.
Druids can quad-kite, whereas a Shaman cannot.
At level 59 Druids can "buy" the AA skill "Dire Charm"
which means they can perma charm an animal mob
that is max level 46. Once you zone you loose the pet
though. Druids also get a pet spell at 55 or so.
Druids get nice teleport spells which aren't needed
so much these days, but still very handy, especially
for evacuation.

I myself prefer Druid having played one to 51 way
back in the day. I got tired and bored of Shaman at 35.

If you play Shaman be prepared to be the buff giver and
please don't skimp on them. We melee appreciate your buffs.