Hi Wrench,
The Tuft & Needle uses multiple layers of polyfoam in both the comfort layers and the support core and the Casper uses a combination of two 1.5" layers of 4 lb memory foam and synthetic latex in their comfort layers over a polyfoam support core so it may come down to which type and combination of materials you would prefer to sleep on. There are also many other options available to you that use either latex or memory foam in the comfort layers that are also in lower budget ranges yet which may also be of interest to you depending on the type of materials you tend to prefer.
Some of the lower budget latex and latex hybrid mattresses that may also be worth considering are listed in post #3 and #4 here and there are also other lower budget polyfoam, memory foam, and innerspring mattresses listed in post #4 here.
There is more about the most important parts of the value of a mattress purchase in post #13 here which may also be useful to help you compare which mattress would be best for you but it boils down to how well you are likely to sleep on each mattress, how long you are likely to sleep well, and then the other parts of your personal value equation that are most important to you (including of course the price and the importance of any return or exchange options you have after a purchase just in case you need them).
Phoenix