I don’t have a food processor, so I can’t give you the comparison except to say that you don’t have to add any additional oil to make prefectly smooth nut butters with the juicer, but I do know some folks do with food processors.
I have a Sampson, so all this is from using that juicer:
You can make nut flours with hard nuts if they’re not roasted. For example, almonds work and hazelnuts work, but soft nuts like cashews and walnuts generally don’t, because they immediately get pasty first pass from the juicer. Basically, you use the ‘mincing cone’ or ‘blank’ or whatever you call it—not the juicing cone. Also, if you have a thingy you put on the nose to add more pressure—sometimes you get extras of different kinds for pasta shapes and such—leave this off entirely. Pass the nuts through once, and you have nut flour. Be careful with almonds, though. Put them through in a continuous stream, but one at a time, or you risk cracking your cone from the pressure. Soft nuts can go in much more quickly. Almonds still don’t take too long, though.
For nut butters, you can make them with roasted or unroasted, but roasted go much faster!! Essentially, you put the same nuts/paste through repeatedly until you have the level of creaminess you want. In this case, rather than leaving the end nozzle thingy off, use the regular one at its tightest setting. Again, put almonds through the first pass in a continuous stream, but one at a time. Maybe two, but any more than that is at your own risk!!! If you roast them, make sure they’re completely cool (even refrigerated) or you will get oil separation. I usually loosen the cones every couple of passes so the suction doesn’t build so much that I can’t get them off when I’m done. Raw almonds take about 7 passes, but roasted about 4. Roasted cashews take about 3-4 passes. Ditto hazelnuts. Walnuts I do raw—they’re so soft, they only take about 2-3 passes, anyway. Ditto pecans. You will LOVE these nut butters!!!!!
To make the word’s greatest nut frostings, refer to the Sicilian Pistachio Cake in RHC. (Don’t have it with me). See the weight of pistachios in the frosting part (in this recipe, it’s the pistachios that you put all over the outside of the cake)? Incorporate that weight of nut butter into ‘that’ amount of completed frosting. The proportion is perfect! I’ve done it with that particular frosting and put my own hazelnut butter into a recipe of caramel Silk Meringue Buttercream—so amazingly delicious!!!! (Note that nut butters have 1/2 the volume of nuts, though—1/2 c. nuts = 1/4 c nut butter).