Hi The Toddler,
While I don’t have all of the covers you mentioned in front of me to be able to compare the “hand” and levels of flexibility, in the first group the one that is most “unlike” the others would be the Savvy Rest, as it would be the least flexible/stiffest of that group. There are variations in the blend/weave/type/certification of cotton and wool used in these covers, but they do all have wool quilted to cotton ticking and use that wool as part of the FR barrier.
In the second group you mentioned, the Luma Sleep uses Tencel, which is a trade name for lyocell. This has a soft “hand” and Luma doesn’t use wool to meet FR standards. The Arizona Premium “bamboo” cover is quilted to wool so it would be similar to the covers your first mentioned, except that bamboo is used to create the viscose dope to make the viscose rayon fiber. Their organic cotton cover is thinner than the bamboo cover and also quilted to wool (see the description at the bottom of this page).
Like everything connected to mattresses … there is rarely one design or component that is inherently “better” than another because it depends on the specific application, components, and design goals of the mattress.
Mattress covers, the fabric they use, the quilting inside them, and their design are an important part of the design and feel of a mattress. There is a much wider range of covers or ticks available to manufacturers that they may wish to use in their mattress for various reasons, including using specific side panels, fabrics, “organic” nature, certifications, “hand” (surface feel), cosmetic features, impact upon the feel of the latex used beneath the cover, and price, just to name a few things.
In very general terms though a loose fitting, thin, or stretchy cover would “allow” the latex layers underneath it to conform to the body shape more closely. Tighter fitting covers that don’t stretch (or mattress protectors or sheets for that matter) that fit too tightly can create a “drum” effect that can also restrict the ability of the latex to compress. On the other hand … a cover that is very loose fitting can stretch and there may be some wrinkles on the sleeping surface which is more of a cosmetic issue than a performance issue.
If you have split layers (a separate layer on each side of the mattress) then it’s usually a good idea to have a quilted cover or a thin layer of material over the “split” top layer to even out the different firmness levels on each side and prevent you from feeling the split itself (see post #2 here).
Those are just a few differences. All of the covers you mentioned are high quality, but which one you preferred would come down to if you had an affinity for a certain feel or componentry.
Phoenix