Well in dungeon groups it boils down to charm. An enchanter can keep a pet permanently charmed for +80-100 dps at 50+, which is a huge win. If the enchanter isn't charming, I give a small edge to the bard (especially an epic bard), although the enchanter can still be very effective with stun/slow/dispell/buffs.
On some raids enchanters can charm to great effect (all planes). On others not so much (pretty much all dragons). Bards are really buffbotting on raids too, it's just that they can't afk because their buffs only last 15 seconds
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As a bard, you will be pressing at minimum 1 key every 3 seconds forever while grouping. Probably much more if you are targeting, pulling, moving around etc.
Really both are fantastic classes with a lot of room for creativity and skill especially when compared with something simple like a warrior or rogue.