That's exactly it; on the rake, the teeth are much farther apart, which means that you have to do several strokes over the same area to take out the same amount of hair that the Furminator removes. I've never used a rake, personally, but we picked up our rescue GSD from the groomer (long story - but basically he was an "outdoor dog" in his first home and so he was VERY dirty, so his foster family wanted him properly groomed before he went home!) when we got him and the groomer showed us how to use the rake. It did take out a lot of undercoat, but it took a lot of strokes to remove it all. Rakes have been around forever, so they are the tried and true method, but personally, for my time and money, I'd pay for a Furminator.
Also, be aware that both a rake and a Furminator can hurt the dog if it's used too many times in a row on the same strip of fur. However, the rake you need to be especially careful with, as the tines on it are not perfectly blunt - you can cut your dog's skin if you push too hard or run it over the same area too many times!
Oh, and one more tool that I love for grooming our GSD is a Zoom Groom by Kong. It is in the shape of a dog and is basically a horse's rubber curry comb; you can find it at most pet stores. It works fantastically to remove loose overcoat from a GSD - if you do use a rake or Furminator on the undercoat, you'll notice that your dog will mainly be shedding the overcoat all over the house - these are the stiffer darker hairs. Neither the rake or Furminator do anything for these hairs, but the Zoom Groom works really well for it. Also, it's like the rubber "fingers" give a skin massage, and dogs seem to LOVE it. But I recommend either using it outdoors, or in the tub while giving your dog a bath because the fur will really be flying with this one! We bought it while spending 3 weeks up at the cottage this past summer, because our GSD was ALWAYS wet from swimming in the lake all the time, so we could never use the Furminator on him!