If the price difference is minimal for the same spec, and I'm pretty sure it is, I see no problem with going for the CSX over a Civic. IMO it is a nicer looking car, though I'm not a big fan of that gen Civic overall. Reminds me of when I was looking to buy a mid nineties Civic Si (won't buy a car without a sunroof, only Civic at that time that came with one) a while ago. Was able to grab a similarly specced Integra (with sunroof of course) for a good bit less than a comparable Civic.
$11k won't go far with that car though, you're going to have a bit of a hard time finding a good condition, low mileage, example at that price. You might want to stay away from the earlier years too as that gen had some teething problems.
Personally, I'm not a fan of how Toyota's drive, not too mention the terrible interiors. Purely subjective of course, give them a test drive and see if it suits you.
My recommendation would by an Acura RSX if you don't mind two doors, do you really use the back seat anyways? Shouldn't be a problem getting a clean '05-07 at ~100k km in your price range. Decently specced, decent performance, and those years are near the end of the product run so all of the little problems are sorted out. TSX's are nice as well, but once again you're going to have a hard time finding a clean, low mileage one at your price range.