An electric boiler replaces the gas (or oil) flame heating of the water in your circulating heating system with direct electric heating of that same water.
Since other losses in the system will be the same (you still have all the usual pipes/radiators/valves/tanks etc) the crucial bit is the efficiency of the heating and cost of the fuel.
The good news is that the electric heating is close to 100% efficient, compared to around 70%-80% for the gas heating.
The bad news is that electricity costs about 4.5 times as much as gas per kwH (except possibly for 'economy 7' overnight - but you won't be using much of that).
So the same amount of heat will cost you about 3.5 times as much to produce by electricity as gas.
So you'd never install an electric boiler if mains gas was a possibility.
Oil (or bottled gas) varies so much in price that the comparison is harder - but currently it is much, much closer to gas than to electricity - so I'd prefer either to an electric boiler.
The only reason I can see for using an electric boiler is as a last resort for a site where neither gas nor oil is feasible (or naked flames are not permitted).
SD