I suspect that a key difference, apart from the voltage being up to 2000-times lower is that domestic cables carry both live and neutral conductors in close proximity so they generate equal and opposite fields. Obviously not the case with overhead cables. Howver, it's many years since I studied physics so am happy to be contradicted by someone appropriately qualified.
The fields given off by the live and neutral conductors only balance out if you are equidistant from the live and neutral. The power lines carried on pylons are three-phase. Assuming the three phases are carrying the same loads, they only exactly balance out if you are equidistant from them - in other words, somewhere in the middle between the three lines. Not a very safe place to be! However, although the fields given off by three phase lines are unlikely to balance out if you are standing under them, in most cases they do tend to balance out better than the fields given off by L&N lines/cables.
If you are in a house under a pylon line, your house will help to shield you from the radiation being given off by the power line. Whereas the ring main and other cabling in your house generally run under the floor-boards and in the ceiling immediately above you, giving you very little shielding.
When you say that the voltage on the pylons is 2000 times greater than that in domestic cables, you are confusing single-phase and three-phase voltages. The 240v domestic single-phase supply is one phase of a 415v three-phase supply. So the voltage on the pylons is only 1000 times higher if you compare like for like.
And anyway, it is the current being carried that is critical when considering the size of the magnetic field being given off. And the reason the grid uses such high voltages, is to minimise the currents being transmitted.