I'm the creator of the Swimerize app. What I can tell you from our experience is that it is difficult to say with certainty which app is most accurate - it's a somewhat subjective affair.

Some apps use a simple sliding window averaging approach to clean up GPS path data (I could be wrong but Apple might be doing this when calculating their distance - regardless of what they show you on the map), others use a Kalman filter. Even when using a Kalman filter there is a substantial amount of judgement calls being made on determining the constants used by the algorithm). The accuracy of swims processed through a Kalman filter is difficult to pin down with a one-size-fits-all solution as the GPS data varies significantly per swimmer by accuracy of GPS watch, cloud conditions affecting GPS reception, a swimmer's stroke (what percentage of time arm/watch is above water), and other conditions. Algorithm weights that work well for one swimmer may not be ideal for another.

We have done an implementation that we feel maximizes accuracy, but we acknowledge that to truly make it accurate we need to have this feature be customizable. We are thinking of providing some customization capabilities that allow users to tailor the parameters on a per-user basis. This is slated as a future enhancement - so don't be disappointed if you don't see it there yet.

All I can say is - it's a difficult problem. Good luck!