The advantages of full-frame 135 format verses cropped format, or APS-C format, have been discussed at great length since the advent of the DSLR. Both formats have their advantages and disadvantages when compared with each other.
I would say the main advantages of the full-frame 135 format are:
(1) Higher resolution in terms of lines per picture height (or width).
(2) Lower noise of the order of one full stop better, on average, across all ISOs, and improved dynamic range, tonal range and color sensitivity.
(3) The option of wider and better-quality wide-angle lenses delivering a wider FoV than is possible with the cropped format.
The advantages of the cropped format are:
(1) Generally lighter and cheaper, especially when using EF-S or DX lenses designed for the smaller format.
(2) Usually higher resolution in terms of lp/mm, as a result of their (usually) higher pixel density.
The consequences of this second advantage of higher resolution is perhaps the main attraction of the cropped format. It allows one to effectively extend the reach of one's longest lens, which is like adding value to a telephoto lens designed for the full-frame format.
For example, the $1,400 Canon 400/F5.6 prime lens on a recent Canon cropped format, say the 18mp 7D, will probably deliver a sharper (or at least equally sharp) image as a $7,000 400/F4 prime on the full-frame 5D3, although the cropped format with the cheaper lens will not match the shallow DoF and low noise of the much more expensive combination.