Just to be clear, the "lagging behind" method means that that you send to your clients an update that is X number of timesteps behind so that the clients are always "lagging behind" the simulation, right?

If that's the case, there is a better explanation than "precision" for your correct choices.

In an RTS, you aren't aiming and the time response is not "real time". That is when you send 10 tanks against 10 hummers, each vehicle will fire on it's own and the path it takes is set by the controlling algorythem and thus both are completely predictable. As well, when both units engage in combat, you won't be doing any "fine tuning" and if you do, a difference of 200 ms won't amount to anything.

But in any game that has human interaction (FPS, RPG), then the movement and aiming is set by the player and thus unpredictable. Under this circumstance, the computer has no idea what you intend to do and thus it has to DR to "best guess".

So human control is one factor. As well, if your game has high inertia (very large mass or very fast), then it become easier to predict where it will be and thus you can adopt a lagg behind method more easily. Therefore a racing game could in principle be well served by a lag behind method because there is little change to the simulation in each frame. In counterdistinction, a game that has low inertia (low mass or slow speeds) would require the DR since it is likely to violently change direction based on collisions and interaction to the point where the lag behind method would fail to capture the correct simulation state.

I just wanted to clarify that "lagging behind" is only a valid technique when there is little human interaction with units and/or high inertia while DR is valid when there is a lot of unpredictable interaction and/or low inertia. It doesn't have to do with the precision but note that a RTS has high inertia and no direct human control while a FPS has low inertia and human control... I think this is a better way of seeing and deciding which routine is better for your game.