Both LaMotte and Taylor makes a drop test for chloride (LaMotte 3156, Lamotte 3155, Taylor K-1766, Taylor K-1771) but it is not really any more accurate than the strips and much harder to use. Getting accurate results with the drop test is tricky at best. The strips are a better alternative, IMHO, and for must users will produce more accurate results. (You won't here me say that about ANY other test strip, btw!)
Also, the titrant in the drop test is silver nitrate, which will cause indelible black stains on the skin and nails if you get any on you!
Both the AquaChek strips and the drop based kits are based on silver nitrate combining with the chloride ions to form silver chloride.
Realize that AquaChek's parent company, Hach, sells these same strips as QuanTab Chloride titrators and they are, in effect, a capillary reverse titration test and not your standard "guess strip".