^^ what Zing said. The different oils do create different "feels" to the soap. A 100% CO soap will be have lots of bubbles and be extremely drying to the skin, unless it has high superfat. A 100% OO soap will take forever to cure, and the lather will have strings of slime (aka "oleic snot").
The awesome thing about designing different recipes is that you are bound to find one that makes your skin happier than another. My skin prefers high lard, low CO, very minimal OO, and goat milk. Powdered goat milk is not very expensive at all, but makes a difference that I can feel. Butters? I can take 'em or leave 'em, but will admit that a touch of shea adds a nice je-ne-sais-quoi to the lather. I'm just too cheap to use it much in soap because I like my recipe just as well without it. I can't use a lot of FOs because they give me headaches.
My husband has eczema and psoriasis. His skin does best with high lard, low CO, no butters, no OO, and some neem oil, with powdered goat milk and colloidal oats as additives.
One of my best friends dislikes high-lard soaps. Her skin loves 80% OO, 15% CO, and 5% castor oil, with goat milk and a very specific FO that makes her nose happy, too.
I could go on, but you get my drift. There is a balance between the one extreme of "soap is a wash-off product that just cleanses," and the other extreme where "skin problems can be cured with soap made from the correct blend of oils, herbs, eye of newt, and powdered rhinoceros horn."
Bottom line, different combinations of oils and additives will make very different soap. Whether you or your soap users care about those differences is a very personal thing. Have fun making small batches and exploring what recipe you like best!