Hi lynndipeitro,
I have no personal experience with any of these covers but post #6 here has more about some of the more general differences between a wool quilted cover and a stretch knit cover.
You could also ask each manufacturer about the more technical specifics of each cover such as the amount or type of wool used, the type and thickness of the fabric used, whether the wool is the only material used as a fire barrier (some wool covers use a blend of wool and other fibers and some mattresses don’t use only wool as the fire barrier), or any other information that may be important to you but this won’t tell you how the cover “feels” in combination with the other layers and components so your conversations with each manufacturer and your “best judgement” are really the only way to know which one you may prefer. Wool is also a more costly material so a wool quilted cover would be more costly than a stretch knit cover.
Again … these types of questions are best asked directly to the manufacturer who will give you the most accurate and up to date information (components can change as new materials and covers become available).
If you mean split top layers where you can have different firmness levels on each side of a king or queen mattress you will find examples of both (split layer and single layer) depending on the manufacturer. In some cases you have a choice between the two. there is more about split layers in post #2 here.
If you mean glue seams then there are some types of latex (such as Talalay) have a glue seam in king size (and other sizes as well). Post #6 here includes some more information about glue seams in latex layers.
Phoenix