Both of them are equally enjoyable. At end game(aka level 70), it depends on what you want to do, pvp or pve. Shamans are very desired in a raiding environment(10man and 25man), whereas Druid usually dominate arena/bg. It is very annoying to kill a healing Druid because they have an instant heal called Swiftmend every 15 seconds, and usually heals them up to full, whereas it is easy to lock down a Shaman and prevent them from healing themselves.
On a leveling difficulty scale, Druid is easier than a Shaman*
Not much choice if you're Alliance, only Dranei. If you're Horde, I'd go with Orcs for Blood Fury(Increases melee attack power by (Level*4)+2 and your damage and healing from spells and effects by (Level*2)+3, but reduces healing effects on you by 50%. Lasts 15 sec.) and Axe Specialization(Expertise with Axes and Two-Handed Axes increased by 5.) Or you can go Tauren for the looks(Mooooo~), Warstomp(Activate to stun up to 5 opponents within 8 yards - lasts 2 sec - 2 min cooldown), and Endurance(Max Health increased by 5%).
For an Alliance Druid, they have no choice but to pick Night Elf. Same thing for a Horde Druid, only one choice, and that is Tauren. Pvp wise, I'd say Alliance Druid has an edge over Horde Druid, since Shadowmeld is OP in arena. But then you could argue Horde Druid has Warstomp and Endurance. Personally I like to be able to stealth without being in Kitty form.
As for spells, you can't really compare the spells each class has.
Healingwise, Druid is a heal-over-time(HoT) class, whereas Shaman is spamming direct heals, such as Chain Heal. In raids, Chain Heal scales incredibly well, top guilds usually bring 3 healing Shamans to raids, compared to 0 to 2 healing Druids.
Melee attack wise, Shamans are really simple to play, and quite fun in my opinion, Flameshock, Earthshock, Stormstrike, then Flameshock whenever debuff falls off, and Earthshock in between Stormstrike cool down. Keeping totem up could be quite challenging for some encounters/people. Feral Druids have it even easier. You also have the choice of tanking in Bear form or Dpsing in Kitty form. But generally, Cat dps is not very impressive.
In terms of magical damage, an Elemental Shaman can really dish out some enormous Lightning Bolts. The only downside is they have really poor spell push back resistance. Same goes for Moonkin Druids, but to a larger degree that besides the Moonkin Aura for increased spell crit, there isn't much they can bring to the table, in terms of raiding.
Also, Shamans have Heroism**(Increases melee, ranged, and spell casting speed by 30% for all party members. Lasts 40 sec.), which is why they are so good.
In the end it comes down to what you want to do and enjoy doing. I narrowed it down to Shaman for pve and Druid for pvp, but there is nothing that says either class can't do the opposite.
Good luck and have fun =]