.bmp is a standard Windows bitmap image format on DOS and Windows-compatible computers. With this option you can choose to use Run-Length-Encoding (RLE) compression, this compression scheme is loseless.
TIFF (Tagged-Image File Format) is used to exchange files between applications and computer platforms. The TIFF format supports LZW compression, a loseless compression method.
I have had some bad experiences with compression programs and now stay away from them. Your mileage may vary.
TIFF is a more universal format, not only between operating systems, but between programs that you might want to import images into.