As with all questions, the answer is: depends.
The ONLY reason I bought my STI over a WRX, is because the STI was being offered for $7k off MSRP back in '08, making it a whole heck of a lot better car than the WRX, but for not much more money. The '08 WRX was also a bit of a flop, too. Soft, uninspiring suspension, 224HP vs '09+ 265HP, plain-Jane body styling (wide-body WRX offered in '11.)
While the THREE limited-slip differentials will be leaps and bounds better than the open front and rear-diff'd WRX, that difference may not make much of a difference if you're never in a situation to use them. I have been, and was absolutely amazed to feel how the car turned a situation that may have been well beyond the safe limits of a WRX (and way beyond your average passenger car) and handled it with ease. Heck, I've only auto-crossed once, and the only reason this newb posted even remotely decent times, is because the STI was able to pick up where my sloppy driving left off.
As far as how those LSD's help in the snow, that's tough to say. With snow tires and the center differential in full lock, I was able to FULL BOOST accelerate up a snowy hill while taking a winter driving course. While the WRX may not have been able to do the same as quickly, it would have been able to at least get you going just as easily. So, for normal driving in the snow, a WRX would behave similarly, and may even perform better if you're able to run narrower, taller snow tires (the all-season tires will definitely provide better traction in the WRX over the STI - with high-performance AS tires, my STI was downright dangerous in the snow, and I got stuck twice!)
Conclusion (things to consider, IMO):
1. The WRX will seem very fast, so unless you're coming from an STI you may not notice the power/torque boost.
2. The WRX has the same wide-body design and looks very similar to the STI, so looks shouldn't be a factor.
3. The WRX will get better gas mileage. I drive very smartly and usually conservatively when there's no room for a-hattery. With a lot of highway driving at my usual speed limit + 5, I'm still only averaging a lifetime gas mileage of between 21 and 22 MPG. All highway, I range from 24-26 MPG at or just below the 65 MPH speed limit, down to 21-22 MPG at 70+ MPH. The STI does NOT like to speed, and even while in I-mode, it sucks down gas.
Granted, the last WRX I had was an '06, but I was able to easily get > 27 MPG on the highway, driving well over the speed limit. Along the Jersey turnpike, I was able to get close to 30 MPG, where as my best in the STI on that same path, my best was 26 MPG.
4. It's a toss up as to which is more reliable. The STI has more robust parts, and will deal a lot better with abuse, but if you're a careful, considerate driver, that may not matter, and a more-reliable WRX motor may prove beneficial.
5. DD-ability definitely goes to the WRX. The clutch is A LOT lighter and the five-speed is much nicer than the clunky, crunchy 6MT. The WRX is also a little quieter.
6. At the edge; however, the STI is a freaking beast. It can literally handle just about anything you can throw at it. Even without any modifications, you can hear the turbo spool, the gears whining and pretty much every other road noise. While this creates what can sometimes be an overwhelming amount of road noise, it also adds a certain visceral connection between man, machine and road that I've never felt in any other car I've owned.
7. For both the WRX and STI, consider the wagon. When the '08 first came out I quoted insurance and it was pretty darned high. Not two weeks later, my insurance company updated their database to include the new '08 hatchback STI, changing from "4DR Sport Sedan to 4DR Sport Wagon." That change in designation from sedan to wagon, at least at that time, dropped the quote by $20/month!
If you have the additional money and it for-sure won't add an appreciable financial burden, that YOU MUST GET THE STI. If you will feel the pinch of the additional cost, then I wouldn't even consider the STI, since the WRX is a really nice package.
ONE MORE THING!!!
The WRX and STI will be the the same for '14, though rumor are rampant that the redesigned WRX and ST will be sold as a MY15. Who knows what exactly will change, but speculation has it that a direct-injected motor will be used to up power and fuel economy, and that both the WRX and STI will split from the Impreza body and be their own animals. It may be worth waiting, to either determine whether the new upgrades are worth it or to take advantage of a deal on out-going models.