So what does it sound like when a differential is going out anyway?

Last few times I've driven the WRX ('02 for reference) it's begun a new noise up front somewhere.  The transmission has always been kinda loud but it's fine.

It's a bit of a roar, for lack of better words, it builds with speed over about 20mph.  It does not change with rpm or different gears.  It's almost definitely up front.  It's definitely more noticeable than it ever might have been before.  The tires are still fairly new and I check the pressures regularly.

I'm thinking either diff or maybe wheel bearing.  I've never had either go bad on me so I have no idea.

Does it change when turning in one direction or the other?  That indicates wheel bearing. 

I just replaced the rear end in my NC Miata.  The symptoms were as follows: 

- Noise that sounded like a jet turbine 

- Started making noise at 20-30 MPH and would increase loudness from there.  

- At 70 MPH with the top up the noise was very loud

- Sometimes I would have a "clunk" when accelerating from a stop 

- RPM made no sound difference 

- Gear selection made no difference

- Steering input made no difference  

- Throttle % would change noise.  WOT would be almost quiet. 0 throttle would be almost quiet.  Partial throttle or cruise was deafening.   

When I got the rear end off the car, the planetary gears had roughly 2-3 mm of in and out play.  This was likely the source of the noise.  

Wheel bearings would change noise depending upon what you are doing with the steering wheel.  i.e. louder or quieter while turning with uniform throttle.  

Just my experience. YMMV.  

I have a good bit of experience with diff failure. It's usually some kind of cyclic tapping or thudding sound. My Samurai's front diff started to make what I'd describe as chain-reeling sound (think drawbridge/castle gate noise, repeated metallic tapping) when it started to fail. Then I got a used replacement that was no good, it started to make a cyclic thudding sound in reverse, similar to what the back of my dad's X-trail started doing about a year ago.

Your noise sounds more like a wheel bearing problem, and Imprezas are known for their achey-breaky wheel bearings, especially in that vintage.

Porbably wheel bearing.   A diff or trans will make different noises dependent on acceleration or neutral throttle or engine braking.  A wheel bearing may (usually) change dependent on side load one way or the other.

I don't have much experience with WRXs but axle noises can be tough.  I've had some that whined when a carrier bearing went and some that sounded like the brakes were dragging with the same problem.

Only real solution I ever found for proper diagnosis is to put someone in it on a lift and have them drive it while you put a dowel to the soft spot in front of your ear and the other end on the knuckles and the diff.  Its hard to pinpoint exactly where things are failing since the sound travels, but you can at least narrow it down to diff or wheel.

I came to suggest driving any Subaru to get an idea of what it sounds like, then I saw the vehicle of concern. Now I'm just surprised that it didn't always sound like that. 

Now I need to drive it again and pay attention when I turn left and right.  That's a start at least.

EDIT:  dumb question, if I jack the front end up and in neutral, would I be able to rotate the wheels and see if one is easier to turn than the other (wheel bearing issue)?

No, but if you spin them pretty fast, you might be able to hear the growling bearing.

I have had success with checking temps on bearing housings. Start with a cold car. Drive for 4-5 minutes at 40-60 mph. Pull over and check the temps of the wheel bearing carriers, diff input and output and drive shaft center bearing if you have one. The guilty bearing will usually be hotter than the rest. 

It helps to have your stopping place already picked out and throw a set of ramps in the back so you can slide under the car.

Wheel bearing will change sound as load changes and you can usually determine which side of the car it's coming from by sound. Diff bearings are harder to track down to a specific bearing, but if one is failed, I'm changing all of them while it's apart or sourcing a used unit. 

Wheel bearings should be relatively easy to diagnose. Make a abrupt left or right turn to transfer vehicle weight side to side. If the noise gets louder, it's the wheel bearing with the most load on it. Ie left turn means right front wheel bearing. 

Diff bearings should change volume with throttle. Floating the throttle at no load, no deceleration should make it quiet. Hard engine braking or acceleration should make diff noise louder. Worn carrier bearings will be a rumble sound, speed dependent, but more so load dependent. 

Jack stand driving diagnosis is tough because the diff may not turn both wheels at the same speed, causing spider gear noise which is normal to a extent. 

I always thought it sounds expensive...