Workout app is not using (or so how I interpret Apples language) GPS to calculate data as I mentioned. Its just using it as a data point to refine your stride length which in turn helps better approximate your distance. So they are not using the same data. As someone pointed out, perhaps on outdoor cycling, it is using GPS since the accelerometer would not be very useful.
I will say that Runkeeper should not be viewed as an official source of GPS data and thus being accurate. I have done 5 tests using Runkeeper, Runmeter, and AW compared against the actual mileage of my tracks using the Footpath app. Whats nice about Footpath compared to Google Maps is that you can draw your paths without having to be straight lines. So if you know that you crossed on a diagonal, you can map it a bit more accurately. I am in NYC and so what problem with GPS is that its harder to get a consistent signal because it bounced off building and or tree cover. I could show you the maps but basically you can observe these problems (which are also related to the GPS capabilities of the iPhone) in how the maps for both RK and RM show me crossing the street or doubling back when in fact i ran in a straight line up one of the avenues. Or on a park run, you can see the GPS jump to the wrong trail for a small portion. In total, these small inconsistencies can add up to a material difference; however other times, the impact is not as great and I will get readings within 0.02 for all three when compared against Footpath.
From my experience so far, I have amassed 9 runs and 15 walks with the watch all using the workout app and the phone. My last 5 activities have been very very close to the Footpath distance whereas the first 5, on avg were off by 0.4. These are all across very similar routes, with 2 outliers when i traveled. I am now about to test how these compare when no phone is being used, more for intellectual curiosity as in reality, i almost always carry my phone with me.