Depends entirely on what you are going to do with the image. .jpeg refers to a file type where image data is compressed with the JPEG algorithm to reduce the size files for publishing digital images either by print or viewing.

Quoted from the introduction of the Wikipedia article:

JPEG (short for Joint Photographic Experts Group) is a commonly used method of lossy compression for digital images, particularly for those images produced by digital photography. The degree of compression can be adjusted, allowing a selectable tradeoff between storage size and image quality. JPEG typically achieves 10:1 compression with little perceptible loss in image quality. Since its introduction in 1992, JPEG has been the most widely used image compression standard in the world, and the most widely used digital image format, with several billion JPEG images produced every day as of 2015.

It compresses 8 bit image data because that exceeds the capability of commonly used monitors and printers. However, jpeg compressed image are not intended for further editing. Lossless compressed TIFF formatted data is useful for storing data intended for further editing and specialized monitors or printing.

If you are publishing the photos via the internet you use jpeg because your viewers wouldn’t know what to do with a tiff. BTW It is unlikely that your viewers are using a calibrated monitor so calibrating your monitor doesn’t help them any way.

TIFF (or PSD) are necessary for further editing at a later time but are much larger to save or send over the internet. Some high end labs can accept tiff files for printing but I don’t know if the final print is worth the cost.

You'd be hard pressed to see any difference between a JPEG saved at 100% and an 8 bit TIFF -- it's very easy to find plenty of difference -- in fact more difference than between a 16 and 8 bit TIFF. The photo below of a towboat (there for reference) was saved as a 16 bit TIFF. I resized it and converted it to 8 bit. I then duplicated that 8 bit TIFF and saved it as a highest quality JPEG. I re-opened the JPEG and placed it (pixel aligned) over the 8 bit TIFF and applied a Difference blend mode -- illustration left.

Repeated the same procedure again starting with the 16 bit TIFF but instead of a JPEG I saved an 8 bit TIFF and then placed the 8 bit TIFF (pixel aligned) over the 16 bit TIFF and applied a Difference blend mode -- illustration right.

Download the illustration and the more you see a uniform tone the less difference there is between the layered images. The conversion to JPEG changed the image more than the conversion to 8 bit TIFF. What's lost in the conversion from 16 bit TIFF to 8 bit TIFF is potential -- potential for further editing specifically.

You'd be hard pressed to see any difference between a JPEG saved at 100% and an 8 bit TIFF -- it's very easy to find plenty of difference -- in fact more difference than between a 16 and 8 bit TIFF. The photo below of a towboat (there for reference) was saved as a 16 bit TIFF. I resized it and converted it to 8 bit. I then duplicated that 8 bit TIFF and saved it as a highest quality JPEG. I re-opened the JPEG and placed it (pixel aligned) over the 8 bit TIFF and applied a Difference blend mode -- illustration left.

Repeated the same procedure again starting with the 16 bit TIFF but instead of a JPEG I saved an 8 bit TIFF and then placed the 8 bit TIFF (pixel aligned) over the 16 bit TIFF and applied a Difference blend mode -- illustration right.

Download the illustration and the more you see a uniform tone the less difference there is between the layered images. The conversion to JPEG changed the image more than the conversion to 8 bit TIFF. What's lost in the conversion from 16 bit TIFF to 8 bit TIFF is potential -- potential for further editing specifically.

I said you’re discarding more data going from 16 bits than in saving 8 bits as a JPEG. Every bit you discard is half the data. With 8 bits you have 256 “steps” in each rgb color channel, from lightest at 0 to pure color at 255, (0,0,0 being white and 255,255,255 being black). With 16 bit channels I Adobe you get 32,769 steps, (not 65,536 as might be expected because Adobe actually implements it as 15 bits plus 1). That means there are essentially 128 steps between each step in an 8 bit channel. When you look at adjacent steps in an 8 bit color channel it’s very difficult and in some cases impossible to see the subtle difference between steps. When you compare the same pixels from a 16 bit image and it converted to 8 bits the difference in each color channel can only be from 0 to about half of an 8 bit step. Big difference in data. Small actual difference.