Hi BBartB,
Welcome to the Mattress Forum! 
The first place I would start your research is the mattress shopping tutorial here which includes all the basic information, steps, and guidelines that can help you make the best possible choice … and more importantly know how and why to avoid the worst ones.
Two of the most important links in the tutorial that I would especially make sure you read are post #2 here which has more about the different ways to choose a suitable mattress (either locally or online) that is the best “match” for you in terms of “comfort” and PPP (Posture and alignment, Pressure relief, and Personal preferences) that can help you assess and minimize the risks of making a choice that doesn’t turn out as well as you hoped for and post #13 here which has more about the most important parts of the “value” of a mattress purchase which can help you make more meaningful quality/value comparisons between mattresses in terms of suitability (how well you will sleep), durability (how long you will sleep well), and the overall value of a mattress compared to your other finalists (based on all the parts of your personal value equation that are most important to you).
I would also avoid all the major brands such as Sealy, Simmons, and Serta (including both of the mattresses you mentioned) and the stores that mainly focus on them (see the guidelines here) because most of the mattresses they make use lower quality and less durable materials that will tend to soften or break down much too quickly relative to the price you paid and the loss of comfort and support as a result of foam softening isn’t covered by a warranty (see post #174 here).
Mattress manufacturers generally try to differentiate their mattress from the mattresses made by other manufacturers and they don’t normally try to “match” another mattress that is made by a different manufacturer so it’s unlikely that you will find a mattress that is specifically designed to “match” either of the two mattresses you mentioned in terms of the specific layers, components, and design. That doesn’t mean that there aren’t other mattresses that would be just as good or even better in terms of “comfort” and PPP (Posture and alignment, Pressure relief, and Personal preferences) … only that they may not have the same “feel”. Different people can also have very different opinions about how two mattresses compare because of differences in their body weight, sleeping style, or individual circumstances and sensitivities so the only way to know how two mattresses compare “for you” will be based on your own careful testing or personal experience.
I would also avoid using another mattress as a “target” (which may not even be the “best” match for you in the first place in “real life” over a longer period of time) and rate every mattress you consider against a common set of criteria based on the parts of your personal value equation that are most important to you.
No matter how comfortable a mattress may feel in a showroom or how well you sleep on it when it is relatively new … there is little value in buying a mattress if the materials inside it are likely to soften or break down prematurely and you lose the comfort and support that was the reason you purchased it and need to buy a new mattress much too quickly relative to the price you paid.
I would always make sure that any mattress you purchase uses higher quality and more durable materials so you have a reasonable expectation that your mattress will maintain the comfort and support that you need to sleep well for a much longer period of time (see this article and the quality/durability guidelines it links to).
Phoenix