Hi pmsmith2032,
There is more information in post #9 here about the different ways that one mattress can “match” or “approximate” another one. Every layer and component in a mattress (including the cover and any quilting materials) will affect the feel and performance of every other layer and component and the mattress “as a whole” so unless you are able to find another mattress that uses exactly the same type of materials, components, cover and quilting, layer thicknesses, layer firmnesses, and overall design (which would be very unlikely) then there really isn’t a reliable way to match one mattress to another one in terms of “comfort”, firmness, and PPP (Posture and alignment, Pressure relief, and your Personal preferences) based on the specifications of the mattresses (even assuming that you can find out all the specifications you would need for both mattresses you are comparing in the first place).
Each mattress category (see here) can include hundreds of different mattresses with a very wide range of different designs, different “feels”, different characteristics, and different firmness levels and will generally include some mattresses that have a design that will be a good “match” for you in terms of “comfort”, firmness, and PPP and others that use the same type of materials and components and are in the same category and may be just as durable but have a different design or firmness level that may be uncomfortable or unsuitable for you to sleep on … even if it uses the same general type of materials and components.
I don’t know of another mattress that uses the same materials and components and that has the same design as the Brooklyn Bedding BestMattressEver so the only way to know how another mattresses that has a different design would compare for you (different people can have different opinions about how two mattresses compare) would be based on your own personal experience with both of them.
The BME would certainly make a great quality/value choice but I would include My Green Mattress/Quality Sleep in your research because they have a range of latex mattresses that you can test in person that would also make great quality/value choices as well.
I’m not sure you are clear between the difference between a box spring and a foundation. A box spring has springs inside it that flex under the mattress and there are very few one sided mattresses today that use them as a support system and in many cases they will invalidate a mattress warranty. Most mattresses in the industry today need a steel or wooden bedframe with a foundation that has minimal to no flex (vs a box spring that flexes) or a platform bed which also has little to no flex under the mattress. There are many in the industry that mix up the terminology between box springs and foundations even though they are very different products.
Any foam mattress with a polyfoam support core will generally do best with a firm, flat, and evenly supportive support surface underneath it that has minimal to no flex under the mattress and for larger sizes with at least one center support beam that has good support to the floor to prevent any sagging in the middle of the mattress. The components (either a bedframe and foundation or a platform bed) need to be strong and durable enough to support the weight of the mattress and the people sleeping on it without some of the parts bending, sagging, shifting, or breaking with extended use. The support surface under the mattress (which may be a solid surface, slats or a steel or wire grid) should have enough surface area to prevent the mattress from sagging through any gaps or spaces in the support surface over time but still allow some airflow under the mattress. If a foundation has a slatted surface then I would suggest that the gaps between any slats are no more than about 5" (with 1 x 3 slats) although I would strongly suggest 4" or less which would be better yet.
There is more information about the different types of support systems (bedframes and foundations or platform beds) that are generally suitable for different types of mattresses and some examples of each of them in post #1 here. I would also keep in mind that these are general guidelines and some manufacturers have requirements that may be different so I would always confirm with the retailer or manufacturer of your mattress that any support system you are planning to use under the specific mattress you purchase meets their warranty requirements and guidelines.
Phoenix