The comparison between the two is, in my honest opinion, just a question of what element you want to play.

The Dragon bloodline is, effectively, a fire-elementalist subclass. Yes, I know you can choose "ice" or "lightning" as your dragon element (poison and acid are non-choices, with 2 to 3 spells each), but there's more to it than that. Thematically speaking, fire is renowned for its raw power and destructive potential, as well as its transformative properties (even if its by setting something aflame) and for reaching skywards. Scales, terror, flight, more damage than others - all appropriate for a fire elementalist. Even if you choose ice or lightning for your element, the bonuses are thematically in line with fire magic more than the other elements. As well, the dragon has the least need of bonus spells, since it has access to so many of the fire spells it could want already.

Now, for the storm soul... Wind, as an element, is known for its flexibility, flight powers, and mobility. From a thematic perspective, the stormsoul is much more appropriate for someone who wants to play a wind elementalist. Not only do we get thunder spells on top of lightning for a more flexible spell list that we benefit from, but just each spell also lets us play something that lets us feel like we're throwing gusts of wind around (speaking of which, I houserule that spells like Gust of Wind also benefit).

On the same matter... ice, from a thematic standpoint, is all about slowing things down. An ice elementalist should be less about inflicting massive damage as much as slowing down targets. Such as per the Slow or Hold spells, such as Ray of Frost's "travel slower" rider effect, etc. A true ice elementalist should have benefits that resonate along such "control" effects as much as fire/dragon gets more "blasty" effects and stormsoul gets "mobility" powers. An ice-themed subclass should be different from the dragon bloodline for that reason, if/when its designed. As well, an ice elementalist should likely have benefit from "water themed" spells, rather than just ice-damage.

That, above, is my opinion on the matter. The dragon and stormsoul are completely different focuses, and the better one depends on personal playstyle and desire. You want a lightning/wind elementalist? Go Stormsoul. Want fire? Take Dragon.

P.S. An acid elementalist would likely resonate along with necrotic energy and undead, while a poison elementalist would involve mind control and confusion spells - an enchanter style, in other words, for poisoning the mind as well as body.

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