Depends on how I wanted it done. Thor would beat back this invasion, but the Doctor would prevent them from(or at least think twice about) invading again.
You’re all asking the wrong questions. It isn’t about the character, it’s about the writer.
Thor, as written by Joss Whedon would be absolutely out of the question. The first half of the invasion would feature Thor falling in love with a beautiful but jaded and bitter princess of the invading aliens and spending all his time in angsty self-doubt. Eventually he’d get around to kicking ass, but cause far too much rampant collateral damage and someone I care very much about would be killed tragically or senselessly. This would leave me wondering if I hadn’t done anything at all if it would have been better or worse.
The Doctor, as written by Steven Moffat, would also be absolutely out of the question. He’d spend all his time barely keeping things together while being both manic and completely incomprehensible, but at the end would get things resolved. During his battle Earth may well be destroyed, everyone enslaved, generations erased from time, and untold suffering caused, only to be wiped out by a timey-wimey, wibbly-wobbly plot device. We(being close to him) would retain the memories of the suffering and live the rest of our lives with PTSD.
Clearly we need to be thinking beyond just the character in making this decision.
Enjoy,
Steven
Where’s the option for movie!Loki?
… yes, I know I have problems. But he’s got that cute little smirk.
Movie-Loki may agree to fuck you (and he’ll probably be good at it), but he’ll also sell you out to the aliens afterwards.
I vote for Thor, the Walt Simonson version. When do I get my lasagna, Skald?
I had two conflicting reactions to this:
- “As if The Doctor would be romantically interested in me anyway”
and - “Threesome!”
Yes, yes, but I meant moral incentives to do *more *than just prod buttock. Initially he’d just stand between the aliens and the town and say some dopey shit like “these humans are under the protection of the Son of Odin, leave now and thou shallt not be harmed !”. He’ll keep himself in check, maybe not go all out until he’s seen just how bad they are or until they push him, that kind of thing. Possibly even insist on face-hammering the aliens one at a time at first. Banter with the Big Bad. Try intimidation before setting the whole ship on electrical fire. Fail to protect people a couple of times, so he’s good and teary-eyed vengeful.
That’s because deep down he’s a good person. And a bit of a twerp (well, admittedly I’m only really familiar with Ultimate Thor, but…).
Original Thor, being a complete idiot with severe anger management issues, will go for the bloodrage-fueled bull rush & overkill NOW.
While Loki is certainly not my favorite, I don’t think I’d toss him out of bed. But I have noticed an amazing preponderance of fangirls for Hiddleston. Don’t get me wrong, I think he’s very attractive, but in a cast MADE for fangirls, it’s funny that everyone likes the bad boy.
Doctor 10. After his performance in the Christmas Invasion, I expect he’d improvise a solution with a borrowed ham sandwich and the elastic from his skivvies, and limit collateral damage to the depopulation of Swindon.
See: previously mentioned problems…
Besides, let’s be honest here, if it’s possible for some sort of hero to get there, it will get solved whether or not I call for help.
Doctor Who? I’d call Doctor Strange.
To Thor, everything resembles a nail. But to the Doctor, not only is the sonic far from all he’s got, it also can do a lot more things (except for hammering, maybe).
Nine.
Because the situation just screams for a bad boy in leather, and Nine certainly got things done during the Time War.
Oh, by the way, did I mention Nine? 
Point of Order: It would seem, since Nine checks his reflection, apparently for this first time in “Rose,” that it was Eight who had gotten things done during the Time War.
This is a trick question right? The answer is Beta Ray Bill.
Doctors Nine and Ten?
Love David Tennant’s Doctor but he didn’t go dark till the end of his run. Christopher Eccleston’s Doctor was a bad ass from the get go. The ninth Doctor seemed much more dangerous. But then again, when such a pretty boy as the tenth Doctor gets angry, that can be pretty intimidating.
Hell, let’s throw in the eleventh Doctor… The enemy will look at him and think he’s too young to be taken seriously. Then he’ll put on a fez and scare the crap out of them and send them running.
Damn I’m torn.
And to save all those lives the whatevers have already captured or killed, the Doctor can just go back and stop them before they get to earth.
And yet it’s caused me to love her 6% more, so, net gain.
D10 because we’d have a fantastic time handling this problem, plus Rose! 
D9 would be okay as I thought he was cool and he seemed to always get the job done with his own certain savoir faire, plus Rose!
If neither of those options is available, can I still have some lasagna?
Untrue. SomeBODY has to shine the Bat-Signal.
That was a fluke, just like that incident with the Kryptonian.