TIFF is a flexible image format that can not only contain pixels/intensities, but also additional information like scale information (X microns/px) or calibration. You can also store overlays in the header part of TIFF file (and it works… hopefully).
Bio-Formats is “The solution for reading proprietary microscopy image data and metadata”. So whenever you use Bio-Formats to open a file that has been generated on a microscope with a vendor software, they are translating information that the vendor puts in its file formats to a standardized form. So opening a vendor file with Bio-Formats and saving it to OME-TIFF will store information, like excitation wavelengths, objectives used during acquisition, temporal information, etc., in a standardized form in the file. This way, you can later re-open that file and take a look at which excitation wavelength the third channel was acquired.
Check the Display OME-XML metadata box to see the information in the standardized form:
Saving your files as plain TIFFs will store some of the meta data, like calibration but not something like excitation wavelength. If you wanted to get that information, you’d have to go back to the original file and open it with Bio-Formats.
Does that make sense?