The press requires a coarser grind as you probably already know, this is about the only difference in the ground coffee prior to brewing. The major advantage the press has over other brewing methods, is the immersion time. This allows more of the coffee oils and flavor to be extracted from the grounds. It also makes for a much much stronger cup of coffee. I favored the press for that reason. The downside is that the press leaves considerable sediment in the cup and the percolator leaves almost none. Could be my grinder doing that too, as I was using a Capressa with conical burrs for a long time, and when I switched over to the percolator I was using a Bunn G1.
Most percolator complaints center around the element getting too hot and boiling the coffee. When the brew is finished I always unplug mine. You might as well know that the Farberware percolators are somewhat inconsistent in temps and brew times. Some just perk better than others. I got several of them and weeded out the ones I liked the best and gave away the rest, and the ones that worked the best were the original ones with the two line address on the bottom. They could have been using better more consistent parts back then, or had better quality control, I don't know, it's just been my experience the early gold badge units are the ones to get.
I use an 8 cup during the week, gives me a morning mug and about 24oz to carry to work. Thermos in the winter, and a mason jar salvaged from a jar of pasta sauce goes in the cooler during the hot months, man, hard to beat ice cold mocha when it's 100+ outside! On the weekends I have a 4 cup at my house, and another 4 cup at gf's house which produce 2 mugs of really good dark brew, they bring out the very best of a FC+ roast.
As far as the sediment, it is a well known fact that coffee is an antioxidant. It has things in it that are very beneficial to the body in addition to being an important source of daily dietary fiber. Drip coffee makers that use a paper filter remove the caffeinol, the sediment, and a good amount of the fiber. It would not surprise me one bit to discover that Americans who use paper filters throw away the best part of their coffee each time they empty the basket. The percolator removes none of the oils, none of the fiber, and the brew has some sediment in it, but nowhere near as much as the french press.
Edit: 2-4 cup vs. 8 cup and 12 cup. All of these units share the same 1000w heating element, and as the laws of physics would have it yes the smaller pots reach their cutoff temperature faster, because there is less water to heat. The two 4 cup pots I have both make very full bodied brews, I guess if I sat down and made a pot in each of the 4 cup and 8 cup pots I could tell some differences if I looked hard enough but honestly all of them get r done in a fine fashion and I don't mind some minor inconsistencies from day to day, keeps things interesting...