It would be a great razor to try,though not sure about $20 any more.a vintage 1960's slim adgustable is just as good and more plentiful,lower prices.
As @brit says, there is little difference in how they shave. As you can see the Fatboy is just a little chunkier, a little heavier and with a slightly shorter handle than the Slim. The "dome" of the heads is slightly different with the Fatboy having the higher, earlier style. Some folks prefer the flatter style of the Slim as it allows slightly better accessibility right under your nose. The only other thing I can think of is that the knob at the handle base of the Fatboy is secured by a screw, whereas Gillette went with a press fit for the Slim and all more recent models. An E4 Fatboy would from 4th quarter 1959. Slims are easier to find, especially in very good condition and because of that are typically priced lower. I have one of each and like them equally.
Is that the protocol? I might buy used Gillette twist open or 3 piece first. Less money. Thank you very much.
If you want a TTO (Twist To Open) Gillette look for an early Super Speed, late 40's or early 50's. They are simple, elegant and provide a smooth shave.
