JPEG is lossy, so the image loses some detail, but the file size may be smaller and compression and extraction can be faster. Wikipedia states, "[It] somewhat reduces the image fidelity... JPEG is also not well suited to files that will undergo multiple edits, as some image quality will usually be lost each time the image is decompressed and recompressed."

TIFF images are larger, but do support lossless ZIP and LZH compression.

If you use or ever plan to use high-end image editing tools (e.g. Adobe Photoshop), TIFF would be preferable. If you're concerned about disk space, JPEG might offer an advantage, though at the expense of image accuracy. JPEG's are also the most convenient form for using on a website or for sharing with friends.

One other option: have the photos scans saved in both formats, or at least in TIFF, and then use any of a number of free (e.g. IrfanView) or commercial utilities to convert to JPEG as you want to share them. It is easy to convert a batch of them. That way you'll always have the maximum-fidelity TIFF to fall back upon.