Initially, I felt a deathclaw would win, but then I thought an Ancient Dragon might win. After really thinking about it, I realized that the focus of different combat styles makes a world of difference. Fallout was designed with ranged (and powerful) combat in mind, with melee a somewhat novel, but useful option. The deathclaws were designed with this in mind. When seeing a deathclaw in Fallout, unless you had tooled your char to be a melee tank, you wanted to back pedal and put as much lead into the beast as possible.
In Skyrim, the combat focus is melee, with two totally different types of ranged combat options, which while comparable to melee to an extent, are not as powerful as the ranged options in Fallout. When encountering a dragon in Skyrim, most folks are going to be able to close in on it and hack away at melee range. In other words, a dragon is designed to be approachable in melee combat, whereas deathclaws are not. Defeating a deathclaw with melee imparts a sense of achievement, unless your char is a higher level char. Defeating a dragon
in any way is designed to feel more like an expectation. Sure, it might be a long battle, depending on your difficulty level setting, your level, and your play type, but it is meant to be accomplished.
I feel like if they had taken the same approach with dragons as they did with deathclaws, we'd all be cursing our screens, throwing mice/controllers, and feeling a lot more accomplished when we killed a dragon. To be honest, I've only been killed by a dragon
once. I can't tell you how many times I've been killed by deathclaws.
To answer the question, as long as the dragon was an ancient, and stuck to the air for the most part, and the deathclaw wasn't anything other than a vanilla deathclaw (no alphas, mothers, or legendary deathclaws), the dragon would win. Otherwise, that would be one dead dragon. My question is this: what shout would the deathclaw unlock with that dragon soul?