They do similar but different things. FP will "abrade" away swirls and minor scratches. It will leave the surface glasslike. I think that FP will provide more gloss than AIO if you are doing a head-to-head comparison but AIO is slicker. FP will not leave any fillers and will be squeeky when you run your fingers on it.
You might think of AIO as polishing by leaving an acrylic "film" that smooths the paint after it has cleaned the surface of contaminants. The upper parts of the layer will carry away the contaminants after it is wiped off and leave the lower part that bonds to the paint and gives a smooth surface. AIO also doesn't have fillers.
Since Klasse twins do not mask any defects on the paint, it is important to really remove swirls and scratches by using polishes that use abrasives. I have had great success using FP or DACP prior to AIO.
Whenever I polish, I use FP to burnish the paint before applying any finish. I never count on FP to do any "cutting" because by the time I get to it, all but the fingernail scratches have been removed. I burnish the paint to get it as shiney as i can before using the K-twins.
FPII will set that mirror shine better than AIO. AIO will add darkness(wetness) and protection to any sealant. That's why I usually use them both together. Sometimes I substitute p21s cleanser for AIO, but I usually use FPII on every detail that needs at least some cleaning/polishing.
