Some, not all, private exchange houses will pay slightly more for checks than cash. I think it has more to do with money laundering than risk of theft. Money changers are well armed. Cash is sometimes easier to convert than traveller's cheques if the money changer doesn't know you.
Karen, you are coming well before the big influx of Dominicans returning home for X-mas with US$. Dominicans like to change with money changers. So much so that I can remember one money changer who was paying less than the banks for US dollars at Christmas time. He simply was getting more dollars than he could convert through his usual channels, so he ran to the bank to collect his premium and stay liquid. Under normal conditions, the change houses pay about 2% to 3% more than the banks or hotel based operations, but this can vary considerably with supply and demand.
If you are talking about converting a lot of money, shop around at the park in San Pedro de Macorix, 10 miles from your hotel. There are three or more change houses there. (Casa de cambio Villa, Pena, or Ramses.) If you are coming as a tourist and just want one or two hundred dollars changed, it probably isn't worth the trouble.
One last suggestion. Change the money yourself at an established operation. Do not change it on the street. Do not give it to someone to change for you. Do not accept help from a local "guide" in showing you where a change house is.