i do not think there is any real difference between these formats with respect to the data, however, some of the sample formats that FITS and XISF can support are probably poorly supported in TIFF (like say, 32b floating point TIFF - not sure how many programs can really open that type of file.)
where they differ is in metadata capabilities. TIFF can probably only support EXIF and other metadata formats that pertain to daylight photography. FITS supports the fits header, which although somewhat poorly constrained, is mainly for storing metadata that is interesting to astronomers. (RA/DEC of target, CCD temperature, astrometric solutions, etc.)
XISF can support fits headers, and also solves some of the problems with the poorly-conceived parts of FITS (like not knowing which corner of an image is represented by the first byte in the file.) XISF can also support pixinsight-specfic metadata, like whether or not there is an STF associated with an image and what the STF parameters are.)
anyway, there is probably not much point in converting to XISF before starting processing. if you are calibrating your images then the ImageCalibration process is going to save its output in XISF anyway, and it can of course read CR2 or FITS or TIFF or what have you...
rob