I have yet to be convinced that a "Kalk Stirrer" is any more effective than simply dumping lime in water and letting it dissolve on its own. I used limewater for 30 years or so but I never had a tank with a huge demand.
Limewater is cheap - CA Reactors are more automatic once dialed in.
Limewater is more likely to cause a negative event
CA Reactor will also replenish Magnesium and a lot of the minor trace elements
Limewater dripped directly into a skimmer will remove Phosphate
Limewater will push PH higher
CA Reactors will push PH lower
The absolute best is to have both. The CO2 added by the CA Reactor is immediately consumed by the limewater drip and keeps the PH stable.
I would advise getting the CA Reactor.