Heat pumps change this a bit, doubling the efficiency (assuming its similar to Sweden), but it varies. So in the ideal case, its roughly the same, in practice slightly less, and with costs it gets complicated and dominated by subsidies and existing infrastructure.
Heat pumps require nearby reservoirs however, land essentially, which is available in suburbs, but can be quite a challenge in dense cities.
But the real problem is the cost of changing the infrastructure, remember its not just getting power instead of gas, its also switching out every heater from fluid based to power based. Switching stoves from gas to power, etc. Its not only a big investment, but a time consuming and inconvenient one.
Even if power prices dropped to half I would not expect this to be particularly fast, and worse still, historically Germany has subsidized directly(with rebates, taxbreaks, etc) and indirectly(nordstrom2... LNG harbors, etc) the gas prices whenever people complain, or just to prevent complaints.
I guess replacing gas in German households will require both electricity prices dropping to around one third or less, and substantial government support. Or a multi decade power price drop to say one tenth or less.