The spring gives you more room for error, but the washers work better and are more consistent.
If your diff is slipping, it's likely either that A) you're using too much diff lube, or B) you're not re-tightening the diff after it breaks in.
Build the diff with all stock parts (you can use AE black grease on the thrust, but it's not absolutely necessary) and as the instruction manual states. Use only enough diff lube to coat the diff balls once popped into the pockets in the gear. As you tighten the diff (1/4-1/2 at a time once the diff holds itself together) work the diff back and forth with your hands in between each turn with the screwdriver.
Tighten until the diff doesn't slip. Use an allen wrench in the slots of each outdrive to hold them still, and try to turn the diff gear. It shouldn't budge! If it does, the diff is slipping.
Put the assembled diff in your truck and start the engine. Leave the truck sitting on the starter box and apply enough throttle to get the tires turning. Hold one tire for 10-15 seconds (which will cause the truck to diff out to the other tire), and then the other tire, switching back and forth 4-5 times. Shut the truck off and tighten your slipper completely. Hold the right rear tire and the spur gear with your right hand and try to turn the left rear tire. It's probably going to turn (this means the diff broke in and loosened up). Tighten the diff in small increments until you can no longer turn the left rear tire using this test. Back the slipper off (usually about five full turns) until you can turn the left rear tire with some effort. You should see the slipper assembly (nut, spring, etc.) turn as you rotate the left rear tire. This guarantees that the slipper will break loose before the diff does, which will stop your diff from melting.
Check the diff every five minutes or so for the first few tanks (in other words, don't go run a half hour on a brand new diff without checking it so it doesn't slip). After that, make it a habit to check that the slipper is slipping before the diff every time you go to run your truck. It takes 10 seconds and will save you from melting diffs.