What is the advantage, if any, to using the low, wide container? Or disadvantages?
First of all, I use the more expensive barrels, and there are many models, and some are quite tall. So "low and wide" alone is not really descriptive. Mine are tall and wide but that makes them also hold more. Mine go up to typically 300 L each. If you make more wine of one variety, then getting simply one tall and wide might actually be cost effective over getting many many Brute cans. Or not. I do not know. It would depend on your local conditions and how much wine you make.
Also to consider:
Brutes are not specifically classified and approved for wine making. The others are (which is why they are more expensive).
Brutes have certain food safety certificates, but they are complex and need puzzling together to see if they actually allow for the use of wine making. And there are some health concerns (see the Rubbermaid web site, as they are very open about different states having different regulations about use of these flexible plastic containers in food processing and needed warning labels -- so inform yourself).
Basically, what does that mean: If you want to use them for your personal wine making, live in California (for example) and want to ignore the carcinogenic warning label, then that is your choice. But you may not be able to sell your wine (legally). The chemicals in the plastic that adds the "flexibility" of the Brutes is the problem there. And thus can create another problem with the more expensive wine making barrels. They lack such toxic chemicals and so are harder. And I had one crack once, catastrophically during a crush. Yep, wine all over the floor. But again, to me, small price to pay to getting really the correct "safer" plastic. That was just one barrel. All my others have lasted me 15 years without issues. So not really a worry, but "it can happen".
In the end, up to you -- it is your wine (as long as you do not give or sell it to others without proper warning about how it was made).
Hope this helps.