Here is a comparison of some of the different washes that can be used for pretzels:
Lye: This is the classic pretzel wash that creates a rich brown sheen with thin crust. To make enough wash for one batch of pretzels, dissolve 1 ounce (about 2 tablespoons) food-grade lye in 1 quart of warm water (add the lye to the water, not the other way around). Wear gloves and goggles while using this wash; lye is caustic and can burn if it comes into contact with your skin or eyes. Place the wash in a shallow glass baking dish and dip the pretzels for about 10 seconds on each side to coat. Shake off any excess lye and place the pretzels on a greased, non-aluminum baking sheet.
Baked baking soda: The flavor from this wash is somewhat similar to lye, but the color isn't as dark or shiny, and the crust isn't as crisp. Harold McGee recommends spreading a layer of baking soda on an aluminum foil-lined baking sheet. Heat the oven between 250 and 300 degrees and bake the soda for 1 hour. To store, keep the soda in a tightly sealed jar so it does not absorb moisture from the air. To make enough wash for 1 batch of pretzels, dissolve 11/3 cups baked soda in 1 quart warm water. Place the wash in a glass bowl and immerse the pretzels for 3 to 4 minutes. Rinse the pretzels in a large bowl of plain water before baking.
Plain baking soda: Probably the easiest alkaline wash to make, it lends a mild tang, though the pretzels are not as crisp or thin, and there is little to no sheen. To make enough for one batch of pretzels, dissolve 1/4 cup soda in 1 quart of water in a small pot. Bring the mixture to a simmer, then remove from heat. Dip the pretzels in the wash for 20 to 30 seconds before baking.
Whole egg: This wash gives great color and sheen, but it does not give the same snap and won't give the pretzels the same flavor as an alkaline wash. To make enough for 1 batch of pretzels, beat 2 eggs in a medium bowl, thinning if desired with a little water. Brush onto the pretzels before baking.
Egg white: This wash gives the pretzels sheen but little to no color and won't give the pretzels the same flavor as an alkaline wash. To make enough for 1 batch of pretzels, beat 2 egg whites in a medium bowl. Brush onto the pretzels before baking.
— Noelle Carter