Can somebody explain to me why I'd want to buy the DCI over the BAA? It's quite a bit more expensive.
Take a look at the datasheet. Two factors are relevant: the sensor's viewing angle (although in your case this might be no concern) and the accuracy (page 30-31). The DCI has an accuracy of 0.1°C within the temperature windows of a human body (35-40°C) where the BAA has 0.5°C. You have to decide if your experiment allows for +/- 0.5°C values or if you need more precision. The resolution of both sensors is identical, so if you just need differential values, you're fine with the BAA. If you're interested in the absolute values you should go with the DCI.