In addition to what John said, the difference will be most pronounced when doing HDR panoramas. Remember that even though a 16-bit file contains twice as much data as an 8-bit file (i.e. there are twice as many bits), the 16-bit file can represent up to 256 times as much information (I say "up to" here because you can always use more data to represent the same amount of information - obviously you can represent 8-bits of information with 16-bits worth of data... in this case the extra bits of data don't actually translate into additional information).
To use a hypothetical example, if your raw files contain 12 effective bits of resolution (after accounting for noise), then converting to an 8-bit workflow will result in a loss of approximately 95% of the information in contained in the original file(s) (2^12 / 2^8 = 2^4 = 16, 1/16 = 0.0625). As John rightly says, this loss of information usually manifests itself most clearly in areas where you would typically like to see smooth gradients, like a blue sky. If you want to think about it this way, if an 8-bit file has 255 values of color for a certain channel (say, blue), the 16-bit file can represent 254 additional colors between each of those steps (so, for example, the 8-bit file could represent 46 and 47, but nothing in between, where the 16-bit file could represent something like 46.02083 and 46.02127).
It is also important to say that this analysis applies to all 8-bit workflows, including 8-bit TIFFs. Compared to an 8-bit TIFF workflow, using JPEGs as a source file would also introduce compression errors, which can be more or less problematic, depending on the composition of the scene.
One other matter to consider when using JPEGs as source files in PTGui concerns control points: namely, JPEG compression can have an adverse effect on control point detection algorithms, resulting in fewer (or poorer) matches. Again, this may or may not matter depending on the composition of the scene, but I occasionally find that PTGui easily matches all images on TIFFs when the same scene fails using JPEGs. As always, your mileage may vary.