Something I thought about the other day, and pretty much immediately came up with an answer to, but wondered if anyone else would share my opinion...
A Dalek's extermination ray would probably kill a drone or two, but their shields would soon adapt, as it's an energy weapon (with apparently one setting) So that would be advantage Borg. However. I don't think that the Borg would view Dalek (either creature or technology) as actually worth assimilating (wouldn't give them anything they don't already have) so I think the Borg would simply destroy the Daleks rather than wasting the resources for assimilation...
I'd still put my money on the Daleks. They're genetically engineered geniuses, dedicated to the sole purpose of destroying everything that isn't Dalek. Sure, the Borg adaptation might throw them a curve ball early on, but I doubt it would be long before the Daleks came up with some sort of remodulation device, or rolled out new weapons. It would be somewhat of the unstoppable force hitting the immovable object though, if those two came into contact with each other!
This character is why I don't play my Romulan any more. Tovan Khev is NOT my BFF! Get him off my bridge!
I'd say the Borg would want to assimilate the Daleks. There's a number of technologies that they have that the Borg would consider worthwhile. Their shield technology is at least worth a look at, and their antigravity may very well be too. But most likely their command of time, space and dimensions is the biggest boon the Borg would want. Sure, the Borg already have time travel technology, but it seems to be rather basic compared to the Dalek's. Not to mention there's the times when Daleks have been in the void between universes. Their knowledge about Time Lord technology alone could warrant assimilation. A little box full of millions of drones sounds like a great incursion device, and knowledge of the shielding the Tardis uses and how to counteract it would be considered worthwhile knowledge. Even their biology is probably unique enough to warrant assimilation. If they consider Ferengi worthwhile targets for their resistance to telepathic probes, they'd consider the Daleks worthwhile for their telepathic network.
As to who would win in an all out war, I dare say it might simply break down to another all out time war should a Borg drone get to assimilate a Dalek, which would then give them access to the entire Dalek network. Otherwise it'd likely just end with the Dalek's trying to delete the Borg from time once it becomes clear that the Borg keep adapting to their weapons. Or building another Cruicible.
Awesome feedback, folks Have to admit, I'd rather overlooked those things that might make a Dalek prove worthy of assimilation I do think that if things were to hit the fan, it would indeed be the unstoppable force against the immovable object, and while the Borg could simply assimilate more troops, the Dalek's time travelling shenanigans could indeed be the winning stratagem.
My opinion: Daleks in a first strike, Borg in a prolonged battle.
A successful first strike and the Borg would never exist to begin with, or at least never exist in a form that could fight back. If the first strike fails (whether defeated by the Borg or interference from another time traveler), assimilation would negate the advantage and it would become a full blown time war. And the Borg will have the advantage in overwhelming force and attrition. They won't do things half way - imagine an episode of Dr. Who, except instead of a phone booth it's a fleet of Borg cubes darkening the skies.
Edit: By "successful first strike" I should specify: The Daleks conceal either their existence or at least their intentions and capabilities from the Borg, and their first attack is meant to erase the Borg from time completely without preamble. Nothing smaller scale, just deciding at first glance that anything except a lethal first strike would result in a war of attrition against an enemy designed to win by attrition.
There were no winners in The Last Great Time War, everyone lost
Yes but they where winning, plus I can count 3 Time Lords that escaped the Time War (The Doctor, The Master, the Corsair), and Millions of Daleks (Last Dalek, Emperor Dalek, Cult of Skaro, Davros and the Crucible, Pangram Daleks, Genesis ARC Daleks, Dalek Parliament, the Daleks on The Asylum).
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JJ. Trek is just as canon and awesome as all other Trek, Get over it.