Doser Pros:
Easy Setup. Your setting it up based on whatever your dosing by hand pretty much. And the system is virtually maintenance free. Your only going to have to calibrate it once every 3-6 months and clean and check the pumps once a year.
Cons:
Bionic is expensive as well as the doser + an extra pump. Its a pricey system. Plus there can be fluctuations if the pumps start to clog up and you don;t check and realize. There is a financial roof your going to see based on calcium consumption in tanks. People that dose using bionic or another 2 part usually don't have extremely heavy SPS tanks. For mixed reefs this is usually the most prefered.
If your looking into one i would go litremeter.
Calcium Reactors
http://www.reefkeeping.com/issues/2002-05/sh/feature/index.php
Pros:
Its the cheaper of the systems, media and Co2 costs pennies, and the reactor will run you a little less than a doser. There is a difference in growth systemwide with cal reactors as well than if you were using bionic. The only places i have seen people require one is on 100g+ heavy SPS tanks because the costs of Bionic just get a little rediculous.
Cons:
You need to know what your doing when setting one up and adjusting it. Its not the easiest thing for most people to grasp technically. Plus the system is labor intensive. You need to monitor both the calc/alk levels as well as the pump as it will get clogged quickly depending what you use as well as the Co2 tank. Its also easier to overdose your tank if something fails compared to a doser with things than can go wrong.
Dosing by hand is the cheapest but your gonna spend every day adding the 2 parts in. I don;t think i need to mention pro's/cons. If you have the money to spend on a calc reactor or a doser you should if your dosing alot. It makes reefing much much more enjoyable when you cut out a daily work activity with the tank as you can spend that time looking at the tank.
It all depends how stocked your tank is. There are people that just do water changes to make up for the nutrient and calc/alk loss because of their low stocked tanks.