If you're not big on the "fags in flags" thing - Mardi Gras is not for you. I don't live too far from Sydney, though I've never actually attended the parade it certainly is exactly what you want to steer clear from, going on your post. I've seen enough news reports (and heard enough from friends) to know the content!
That said - if you're not big on crowds then definitely avoid both! Mardi Gras is huge in the areas of the town the parade visits, and New Years positively takes over the entire place.
I would recommend New Year though, the fireworks are brilliant, partying starts fairly early and the atmosphere is fantastic. Plus, we celebrate the New Year quite a bit ahead of the (most of the) rest of the world, which is a nice little feeling!