I do not have the depth of formal training that Shawnee has but I have done a lot of reading on my own. That said, my impression is that the jury is still out on how much of the therapeutic properties survive saponification. To be prudent, I keep my use rates relatively low as if nothing is lost. And I avoid oils like wintergreen and sweet birch which are potentially very dangerous in relatively low concentrations. Additionally, spicy EOs like cinnamon and clove are potentially skin irritants, including in soap, unless used at very small %
There are many, many threads on this subject so if you do a search on FO vs EO you are likely to find a lot of information here.
Pros and cons in my experience, briefly:
FO pros:
Made in a lab so product is consistent across batches and tested for skin safety
Can get scents that are not found in EO form - foody and fruit scents, for example.
Can get scents that are prohibitively expensive/endangered/extinct - sandalwood, rosewood, rose, musk, etc.
Can be stronger and longer-lasting than some EOs.
Cons:
allergies or reactions in some end users.
Some make me feel a bit ill (honey FOs in particular).
Prejudice against artificial scents.
More likely to morph in contact with lye than EO.
EOs:
Pros:
Scent quality. This is subjective, but I prefer the smell of EOs.
They are derived from natural sources.
There "may" be therapeutic effects in soap. There are therapeutic effects in leave on products.
Most do not cause seizing or ricing in soap. Some exceptions: spicey EOs (cinnamon leaf, clove, black pepper) or florals (ylang)
Cons:
EOs involve large quantities of plant matter to make. There can be environmental degradation consequences in their manufacture.
There is more limited variety than with FOs.
I would like to conclude that it is a misperception that FO is always cheaper than EO. You can find many EOs for 20-25 dollars per pound. You can also find FOs for over $50 per pound. If you want sandalwood or rose otto EO, sure that will be hideously expensive. But within the $20-50/lb range, I find a lot to choose from - mints, herbs, woods, spices, citruses. My splurges are patchouli, cardamom, and fresh ginger and as I use them in blends, the upcharge is not too bad.
I do use some FO but typically single notes for blending that are impossible/too expensive to get in EO form - vanilla, coffee, sandalwood, rose, jasmine, amber, coconut, etc.
Hope this helps!