I grew up in between the two (Hale Center), so I have some opinions.
Dust level Lubbock >>>>>>>> Dust level Amarillo. Lubbock's surrounding land is probably 75% cropland, and 90% of that is cotton. From December to May, that means almost "0" ground cover. Also, the soil itself has more sand than the soil further north, so March in Lubbock is horrid.
Amarillo has probably <50% crop land surrounding it, the rest is grassland that does not blow. Of the crop land <20% is cotton, and of the remaining 80%, probably 50% of that is winter wheat, which does not blow in the spring. Corn and sorghum (the other 50%) leave good residue in the soil, that makes it much less likely to blow in the spring.