Joe - the difference is in the development of "maturity" in the substrate. peat in the filter has zero effect on that. If you want tannins and humic acid in the water column, the filter use is the way to go (I do not). The substrate use of peat and mulm (as Tom Barr, Tempest, and I have tried to point out, apparently unsuccessfully) is to get the plants started without the normal and expected new tank lag time before good growth and normal development. The use of both materials all but completely erases the normal and expected start-up period, being more like a simple plant move within an established tank. The use of either will help.
Tom has not to my knowledge put a hard figure on his use (I had to rough guess from his "handful"). But I'm a detail nut, so my use is a measured 1/2-2/3 cup of ground peat per square foot of tank bottom. That is a 1/2-2/3 cup measure, not packed, knifed off to level, spread and mixed into the lowest <1" of substrate. The different volumes are based in part on the intended plantings - if deep substrate and/or many crypts, it is the large volume - I don't think that is particularly sensitive. Whether or not that is a large amount is subjective, but it does not tannin-stain the water to any noticeable degree, nor do I see peat fibers on top of the substrate. I normally use about 4" substrate depths on tanks >12" tall, so it pretty deeply buried. During and after a large scale replanting (a rare thing in my tanks), I have some suspended mulm, but it will settle or be filtered out within less than an hour.