Retaining heat and the type of heating source are different things. A well insulated building will retain heat regardless of where that heat came from.
Also, a big slab of concrete will indeed contain quite a bit of heat - but then the heat input to the room from that slab is uncontrolled. In some respects, the worst thing is a big heavy slab because it stores a lot of heat so it can't be turned down quickly. That's a problem with night storage heaters, because even though they have a damper to control air flow based on room temperature, to give the best results they need adjusting every day to suit expected heat demand for the following day - otherwise you either under-heat on cold days or over-heat on hot days.
Similarly, with a big heavy slab, yes you can store heat from off-peak lecky. But unless the room heat loss doesn't drop below the heat input rate from the slab to the room, then you'll end up with the room too hot. In practical terms you'll get more heat in the room in the morning (slab is hot), and less in the evening when it's typically most needed in a domestic environment because the slab will already have lost some of it's heat. Of course, a really massive slab will lose less temperature during the day for a given heat loss - but the flipside is that control operates over an even longer timescale.
As others have said, you may be better storing (at least some of your heat) in a wet system that can be easily controlled to output the heat where you want it when you want it. But that does need quite a large tank of water.
If you have rooms with a significant solar input (big windows, especially south facing) then you'll have serious over-heating problems (on sunny days) with a big slab of heated concrete.
?‍
?‍
