Mainly location. One is by the kids area (which we're well past age-wise), the one we always seem to get is I think 11, which is sort by the wave pool and not all that private. It "looks" like one of the normal covered structures (because it is, just made into a patio) but is in a relatively high traffic area not near other patios. Disney's tinkered with various plants/cloaking devices and such over time around, but I just don't enjoy it.
Many of the standard patios are along high traffic paths too, but to me they are generally more cozy/comfortable for our needs.
The premium ones do allow you to stay in them in inclement weather vs standard, but to me that's not usually a material thing.
Granted we're also usually a party of four so don't necessarily need the bigger space either.
The TL shacks have more 'bang for the buck' as you go up to the different tiers in terms of space, amenities, furniture type, etc (there are also a lot more of them), which BB doesn't really have with their above-standard patios.
Small caveat in case Disney has made any changes to patios during the current refurbishment closure. They do seem to sometimes tweak these upcharge things to add more ways for all of us to spend money during the off seasons.