As mentioned below, total weight is a big part. If it's a solitaire, it's an I3 clarity with horrible color and cut. You can get 3 carats for under 20 if the quality is that bad. If you have a ring with 1-1.5 total carat weight of smaller melee diamonds, they can be almost worthless depending on quality.
Either way, if it's a $200 ring, the sentimental meaning of it is priceless. It hurts the victim just as much, sometimes more if the ring isn't worth much. I think that's the worst part of all this. Loosing your engagement ring to theft is just a horrible feeling, and the suspect needs to be pretty heartless.