Choose druid I got both geared. Though shamans are fun. Druids, no matter what spec got tons of utility, survivability, awesome mobility and insane off heals plus they are the only healing class and caster dps that can stealth like rogues which will come in handy in some situations especially when you are a nightelf. or you can roll both. Gearing is so damn easy in mop you can enjoy both class.
I can't answer you based on the current bugs on MoP, but I can answer in case of everything working 100%.
PvE;
AoE DPS, nothing beats an Ele Shaman. Ele Shamans also have really nice raid/group support utility spells.
Outside of that, a Balance Druid should perform better, especially on single-target fights.
Resto Shamans were generally considered to be the bottom-end healer, but like Ele Shamans, their utilities are really good, so they were still taken. The optimal healers were Holydins, RDruids and Disc Priests. Remaining heal spaces being usually filled with Shamans and sometimes Monks. Holy Priests were really unpopular for the most part.
PvP;
Balance Druids really hurt, but Ele Shams can perform decently damage-wise, but brings better team utility. Both would perform decently.
RDruid was considered the "best" pvp healer along with Holydins (Holydins having the strongest throughput), mainly because of their ridiculous mobility. Being able to stick to a RDruid was more or less impossible for any class.
For healing bgs, MoP resto druid is my favorite spec of any expansion. There's just a ridiculous amount of things you can do to get melee off you, which you really need on private servers in particular when some are geared to the teeth. So much more fun doing bgs on my MoP resto druid than my Cata and WOTLK one.