Druid is probably better suited for BGs, especially puglife. You're slippery, rdruid has the best burst heals in the bracket, bearform makes you tanky as hell, you can cover huge areas quickly, and your damage output is respectable. If you get caught out alone, you can probably also get to safety between bear form, swiftmend and dash. If you play like a dumbass like me, druid (especially resto) is super forgiving.
Shaman is definitely better suited towards arena and if you're playing with friends/guildies who can take advantage of your utility. Windshear is great 1v1 and in team fights where your team is aware enough to take advantage of it. But solo que, it can be frustrating to kick a healer and see your dps just... farting around. Dropping a totem to split an EFC from his heals is slick as hell unless your DPS is busy trying play defense for a flag thats no longer in base. but when you get a chance to do cool shit, you can do some really cool shit.