Just a dumb question, but how would the 8" coil be more useful than the 11"? To picture a 8" coil, just take some 1" or 3/4 " masking tape and put it around the edge of your 11"(double up to remove 2 inches), personally I do not see any advantage for tight areas, for those I would use the 6"
To illustrate the advantage of the 8" (actually 8"x5" coil) vs. the 6" round vs. 11", need to go over some DD coil fundamentals, elliptical vs. round coils, and the three or four characteristics of DD coils that are important - namely, depth, swing width, swing coverage, and weight and how round vs. elliptical coils trade of these characteristics. Concentric and coaxial coils are a different animal and a the coil size comparison is completely different because the detection field is a conical rather than a vertical slice into the ground like DD's, but since there are no concentric coils available for Vanquish or Equinox, I am not going to talk about those at all.
A DD coil (think of two D shaped coils placed back-to-back with the vertical part of the D's overlapping slightly). Where the D's overlap is in the center spine area of the coil and is where the sensitive area of the coil is. While there is a small amount of edge sensitivity, your target is primarily detected when the center spine runs across the target (side-to-side). The target is detected with approximate equal strength along the entire length of the center spine and then the signal drops off at either end. That is how you can pinpoint by edging the target off either the toe (front) or heel (back) edge of the coil. Since primarily only the center spine of the coil is sensitive to targets, the diameter size of the coil doesn't necessarily determine side-to-side separation since all DD's have roughly the same active width of about 1/2 to 1.5 inches. But a smaller coil will have less targets that can show up under the center spine at any point and a smaller coil can be swung side-to-side in tight situations such as around playground equipment, near vegetation, and around structures. Of course, the trade-off for a smaller diameter round coil, is depth as explained below.
For a round DD coil, the coil diameter roughly determines its depth capability. So the 11" Equinox coil has a nominal target depth capability for a coin-sized, high conductive target of around 11" at a nominal operating frequency of about 10 khz. It can be either more or less depending a number of other factors including soil conductivity, moisture, mineralization, actual operating frequency, target profile (footprint), target mass, and target metallic composition.
For elliptical coils, such as the 8"x5" Vanquish (V8) coil, the depth is determined roughly by the width dimension, so in this case, it would perform similar to a 5-inch round coil. Or perhaps slightly less depth than the 6" round Equinox coil. However, the advantage of the 8"x5" elliptical coil vs. a 5" round or 6" round coil is that you gain the advantage of being able to swing side-to-side in tight spots like either the 5" or 6" round coils but you get the vertical swing coverage of an 8" coil. This means you don't have to tiptoe around a site making sure you get overlapping swing coverage. On the 6" round coil, you probably want to take about 5" forward steps to make sure you get overlapping swing coverage as you move forward. With the 8x5" coil, you can take 7" steps. It makes a BIG difference in how fast you can cover the area but also allows you to have the light weight similar to the 6" round coil (because it is not an 8" round coil) and the ability to get into tight spots where your side-to-side swing width is limited. So it is really not about separation but ability to swing in tight spots, light weight, and decent swing coverage. Separation is not really a function of the coil (other than smaller coils will have fewer targets under them in high target density situations), but more a function of the recovery speed of the detector.
For me, the Vanquish 10x7 (V10) coil seems to be ideal. With 10" of swing coverage and 7" of depth. I like the 12x9 (V12) stock coil of the 540 too.
Those are ideal coin and relic coil dimensions in my opinion. 7 to 9" of nominal depth and 10 to 12" of swing coverage so that you can take normal steps while guaranteeing swing coverage with both of those coils weighing less than the 11" round coil and not giving up much depth.
I am also starting to get some "in the know" folks hinting at the fact that the Vanquish coils will LIKELY be compatible with Equinox, so now my money is on Equinox compatibility.
If I'm wrong, no biggie. I can and will live with the existing Equinox coil options. But the Vanquish coils, if compatible with Equinox, really fill in an Equinox accessory coil gap that has existed ever since the Equinox accessory coils were released last year. Especially, since it appears no third parties are involved in making coils for Equinox, for whatever reason.
HTH