It's cheaper to heat the water tank with the gas. However - I haven't compared that to heating with just the sink option. I've checked the appliance calculator on the esb web site and they don't have it listed. I don't have easy access to my meter to check. Based on the appliance calculator to heat one tank a day from cold with the electric emersion is 68 euro per 2 months!
However, really you're comparing the cost of heating one tank with gas to heating the tank with electricity. It's easy to check the meter for the time to heat up the tank with each. It will be approximated with the electric (take away roughly the other appliances by looking at the average)
For me there is a 5x difference in cost, but that's comparing the figures on the esb site for a full taken with my own metering for 15 min with the gas - doesn't heat it fully, but sufficient for me. So it's not an apples to apples comparison - but good enough that I'm using gas! - My boiler is 10+ years old, really not that efficient, but even with that, far cheaper.
If you want hot water check the following:
Check thermostat in hot water tank - no point in over heating water
Check insulation - pipes, lagging jacket - or factory insulted tank far better - this won't reduce price of heating tank, but less re-heats required.
Just heat the water, don't heat the radiators - can easily switch between them.
Ideally:
Is solar an option?
If not, get a high efficiency gas condenser boiler (20-30% more efficient)
Consider a boiler that heats the water on demand instead of a hot water tank. More expensive than standard boiler - but may save you in the longer term.