What could cause one brand of carbonated water to be superiorly carbonated compared to another?
Carbonated water is supersaturated in carbon dioxide, and the only thing preventing all that excess $\ce{CO2}$ from bursting out all at once is the lack of nucleation sites for $\ce{CO2}$ bubbles to form. These nucleation sites can be almost any solid (including the sides of the container to some degree) from undissolved salts to soil particles or tiny particles of most anything.  

The most likely reason for the formation of such a copious amount of bubbles forming in the cheap water is the presence of a large amount of undissolved solids relative to the more expensive waters. Depending on the product, one step of the processing of carbonated water is filtering in order to make the product appear clearer and more sparkly (and maybe to prevent rapid formation of $\ce{CO2}$ bubbles). Of course this process costs money, and it is likely that the cheaper brand either skips the filtration process or uses a much less efficient (and cheaper) process.