I see 2 opportunities for how the "fizz" behaves. The easy one is pressure, and likely, you'll have no control over that. More pressure, more fizz. Something to definitely look for is a dip tube that goes all the way to the bottom of the bottle so that it'll carbonate from the bottom up. Secondly, the gas itself. Generally, I'd expect it to be pure CO(2) (what I use in my kegerator.) There's a variant called beer gas which is partially nitrogen, and that gives a rather "creamy" appearance and mouth feel. I guess that it's possible that there are additives in the syrups for head retention, but by & large, the carbonation pressure is going to determine the fizzy level. I don't see that how a vessel is sealed will matter, as long as it holds pressure.
It doesn't surprise me in the least that SodaStream will push very hard to lock you in to buying their VERY expensive cartridges, and if you have to buy a new SodaStream periodically, ya know, so be it.