I will start by a parallel with printing photos. Having a resolution of 300 ppi (pixels per inch) is relatively standard. It means that 300 pixels of a digital picture will be printed on one inch. It is common to assume that details are conserved with this resolution.

So if the original painting is about 30*21 inch (like the Mona Lisa), you will need the equivalent of 30*300*21*300 pixels = 56.7 million pixels which is a relatively big picture (as modern camera images are around 20 million). Now if each pixel is coded on 24 bits (8 bit per channel, a channel being red, green or blue), the uncompressed file size should be 56,700,000*24 = 1,360,800,000 bits = 162 MB.

As you can see, a lot of assumptions are required to estimate the uncompressed file size: original painting size, color depth (precision of the color - here 24 bits per pixel), ppi needed in regard of the level of wanted details.... Moreover, JPEG allows different levels of compression and its performance depends on the image. => We can't say much without more information.

If it's difficult to have more information about the 2 options you have and assuming money and disk space are not a factor, my advice will be to go for the TIFF (you can always convert it to JPEG later). If there is a significant price difference and if the original picture have similar dimension of Mona Lisa, the JPEG should be enough for your need (more about it in the last paragraph).

For your information, my grand mother has only used JPEG to reproduce painting so far and even with a few MB JPEG, you can see the brushstrokes (try with Google image search).

If you want to know the difference between JPEG and TIFF, you can start here: Should I save an image as png, jpeg or bmp?

By the way, I assume that both images have the same resolution (pixels per inch) but that the JPEG file is smaller thanks to the compression. Indeed, a compression ratio of 10 to 1 going from TIFF to JPEG is common with pictures and usually provides an image of "high" to "very high" quality. In your case, you have a ratio of about 6, which should ensure a high quality.