As long as you stick to a good brand, “a filter is a filter” – the differences are negligible, and many hot tub brands share the same filter manufacturer. Four filters won’t make your hot tub 4x cleaner – more filters only mean more hassle and more expenses. Filters with a larger surface do the same job as a smaller filter. The only difference is that if you have a tiny filter, you may have to clean it more often.
What matters more than brand or size, is how well the water is circulated (see 4-D: Engineering). Some hot tub models suck more gallons per minute through the filter chamber than others. Some brands are specifically designed to churn the water in such a way that it swirls and mixes things up better than others, minimizing dead zones on the hot tub floor. bottom where water and debris escape the intake/outflow current.
The surface skimmers are supposed to sip the “floaties” (dandruff, hair, body oil, etc.) from the water surface, into the filter chamber. A poorly designed tub has contours and water currents that create back-eddies that trap the floaties in the corners and seat contours, and can cause a “ring around the tub”. instead of being slurped into the filter. Well-planned water flow intentionally creates a current that sweeps the surface floaties into the surface skimmers to be slurped into the filter.

A good brand will pay attention to how the water flows, both at the surface and underneath, and will engineer the arterial systems in such a way that it cleans the water better. So, although good filtration is important as explained above, the cartridge style hardly matters.