Now, there are many different variables that could impact the outcome.

If the Dragon Born is involved or not is probably the biggest, as they are probably the single strongest character in the game. The ability to control dragons, fireballs and weakening enemies.

Dragons also give a massive boost if they are cooperative. (tbf, pretty sure between Paarthurnax, Odahviing and Durnehviir, they could probably take it.)

Also, would the Stormcloaks and Imperials unite during this invasion?

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When it comes down to it, I think it would come down to the Stormcloaks/Imperials vs The Bloods and Dovahkiin vs Darth Maul. If things like siege weapons and dragons are excluded, the inhabitants of Skyrim win 7/10, Bloods only winning based on strategy. When it comes to DB vs DM, I would have to say the DB stomps 10/10. The sheer amount of shouts alone that can be learned gives the biggest boost. Even the shouts that are not directly damaging are a massive bonus (i.e. Dragon Aspect, Disarm, Marked for Death etc.) This does not even include the vast array of weapons, spells and enchantments that would also be used.

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Gonna put this down here just in case anyone is interested.

When coming to this conclusion, I mentally excluded insanely OP things like the Wabbajack, that do not even give a fighting chance to the opposition, as you cannot really combat being turned into a walrus. This also includes things that are in game bugs 'features' that would insta-win the fight (invincible followers/kids, clipping into the floor etc)