I’ve been looking at The Futon Shop’s (https://www.thefutonshop.com/) shikifuton options and I’m not sure whether to go with the latex core surrounded by wool (https://www.thefutonshop.com/all-natural-latex-and-wool-shikibuton-mattress/) or wool and cotton (https://www.thefutonshop.com/wool-shiki-futon-folding-mattress/). The wool and cotton one goes up to seven inches thick while the latex one is limited to three. What would the relative strengths of each choice be?
Hi Zehuij,
Welcome to the Mattress Forum! 
While this site focuses mainly upon mattresses, and not futons, there is a bit more general information about futons in post #2 here.
The principles for choosing a product certainly apply to futons as well as mattresses, although futons will be a bit more limited in comfort and support choices. The materials used by The Futon Shop certainly seem to be of a higher quality.
The wool/latex futon certainly is thinner and in the “soft” range, and it can be rolled up and stored when not in use. It’s a much more traditional “mat” style and is often used on top of another futon or layered two at a time. The wool/organic, in the thicker 7" version, could commonly be used as an every-night sleeping futon, but it will of course have a different feel from the thinner futon with the latex core. The wool futon will over time become firmer and impress a bit more with use. (wool can commonly compress about 30% of its original height, depending upon its original state of compression). The Futon Shop rates the durability of the futon with latex at about twice the time of the wool/cotton futon.
It really comes down to your own personal preference, which of course I can’t predict, as there are too many unknowns, variables, and personal preferences involved in choosing a futon for someone else to make specific suggestions based on specs (either yours or a futon) or theory at a distance that can possible be more accurate than your own careful and objective testing (using the testing guidelines in the tutorial post) which is always the most reliable way to predict which mattress will be the best match for you in terms of PPP (see mattress firmness/comfort levels in post #2 here).
If you can’t test these items in person, then your next best step would be a detailed phone call with The Futon Shop. Their detailed knowledge of their futons and how they fit with different body types and sleeping positions, along with a customer base of many people that they can use as reference points, as well as any exchange/return options after a purchase can help lower the risk of an online purchase (they do offer a 30-day comfort guarantee).
I hope that information is helpful to you.
Phoenix