Additionally, carbonating a half bottle means there's a much bigger head space of compressible air to fill, which means you could potentially fit much more CO2 into the bottle that's only partially filled with liquid.
If you have the floor space and wherewithal, I recommend neither the SodaStream or the iSI (for carbonation, that is) as both are expensive in terms of ongoing costs. We converted a chest freezer (although you could also just use a refrigerator) with a tap. 10- or 20-lb tank of CO2 --> regulator --> corny keg filled with water == 5 gallons of fizzy water on tap at a time. We have two kegs for water, so that when one is emptied, we just pop the hose over (simple ball joint so it takes five seconds) and refill the other tank. It will carbonate on its own in a day or two, and there's never any kind of risk.
A 5-gallon keg full of water is heavy, though, so that's a consideration. If strength is an issue, you can use 1- or 3- gallon kegs, as well, or even just buy a carbonator cap and carb your own 2L bottles of cold water.
More expensive (but still lower TCO) would be to install a used carbonator. This whole setup is worth it for us because we drink, like, obscene amounts of fizzy water. At least 5 gallons a week or so.