Both methods can work well if properly set up. Calcium reactors use a fair bit of electricity to run as they run 24/7, the initial cost is high and you really need a PH probe for the reactor & controller to keep it running optimally. Ca reactors tend to drive the PH down.
Dosing is lower initial cost, is easly adjusted as you system changes, you can dose much more then just ALK & Ca, the cost of suplements can vary drasticly depending on what you use. Ready made mixes can add up quickly and are expensive to ship for mostly water. Or you can make your own using Randy's 2 part recipe. I have 50 pound buckets of calcium cloride for only $40, which will make enough to last most people several years. Large bags of Baking baking soda are available cheap at Costco and other places.
Get good dosing pumps for reliability. If your on a real budget, I have used aqua lifter pumps controled by a Neptune controller in the past. Older controllers can be purchased cheap. You don't need fancy dosing containers, if your on a tight budget. Plastic soda bottles or 5 gallon water jugs can be used depending on the size of your system.
I have used both methods over the years, as well as dosed Kalk. What ever method you use, you need to measure your parameters often until you get it dialed in. For calcium reactor you must bring your levels up and in balance first. Otherwise it is much harder to get working properly and impossible to balance. This is also a good idea if your dosing as well.
On my 300 gallon I dose because I like the control it gives me and the consistency.: I cirrently dose ALK, Ca, Mag, Stountium, Potassium, Viniger & Iron. Not all are automatically dosed yet. I prefer the control and reliability of my Neptune controllers over the dosing pumps with built in controllers that I have tried.