I find him to be in a fairly good spot. Of course, I've had much better experiences with him when playing in a group of people i know, but he works well enough outside that.
One of a few things would put him in a better spot though...
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Faster chime spawns at the start of the game
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Longer range on Q
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Fast speed on Q
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More exp from chimes
Outside of that, I don't build AP on him, so I'm not seeing heal or damage increases, so yes, Soraka has the potential to dish out greater damage, especially with her E, but he really isn't far behind and has much better autos.
His heals are not and should not be Soraka level, but they are quite strong, even without allowing his heal to fully charge for full strength.
Again, without AP to boost his heal, I had no problem out healing an opposing Soraka. Her health cost and good poke/positioning made her heals essentially useless while my ADC continued on effortlessly.
He's still new. Players are still going to try and figure him out, practice landing and timing his abilities just right, as well as throwing him into the fire in some odd roles. I've seen ADC Bard completely dominate a couple of games.
I'm sure Riot has an eye on him though.