The problem is probably that you can't always have to same range of colours in a JPEG image that you can in a tiff image. TIFF images have an 8 or (usually) 16bit colour palette (erg 2^8 or 2^16 colours). Most JPEG encoders only support 8bit colour. However the encoding algorithms vary greatly from software package to package.
If you can't find another package with more suitable colour support, then i'd recomend reducing the colour depth of the TIFF into 8bit, which should provide you with some sort of choices.
The other factor could be the compression. TIFF files can be uncompressed, lossless compressed, or lossy-compressed.
JPG files are all lossy-compressed based on a grid. Blocky artifacts and softness at boundaries are sometimes caused by having the compression ration of the JPEG a bit to high, overly compressing the file.