So you mean you would pay an extra €2000?
In that case, I would definitely go for the heat pump.
Assuming a 20-year lifespan, it would probably come out ahead given today's energy prices.
Take a look at a full cost calculation.
For example, the basic fee for the gas meter, chimney sweep, (chimney if no fireplace is planned), maintenance is cheaper and less frequent.
But: the heat pump needs to be properly planned and adjusted correctly by you once in winter.