Proton and Carbon NMR are the spectra that differ in many ways.

Sensitivity

In terms of spectroscopic sensitivity carbon-13, NMR is a much less sensitive technique because of two factors, the gyromagnetic ratio, and natural abundance.

The gyromagnetic ratio is another parameter that determines this value. It is represented by the constant gamma and is a characteristic of each isotope. The sensitivity of a nucleus in NMR depends on gamma. The higher the value of gamma, the higher the sensitivity and vice versa.

The value of gamma for carbon-13 nucleus is 9.6 and for hydrogen-1 it is 27.4.

The natural abundance of carbon-13 is 1.1% whereas for Hydrogen-1 it is 99.9%. The theory behind it is simple, there are more hydrogen atoms contains in a sample and so easier to detect.

Coupling

You don't see coupling in Carbon-13 NMR because of the low natural abundance. There are no carbons that can come close enough to one another in proximity for coupling.

This is why we don't see splitting in the spectrum. In the case of proton NMR, we see hydrogen coupling and hence splitting patterns in the peak.

Figure 1 shows an example of what peak splitting looks like in a proton NMR spectrum.

Proton NMR spectrum of ethanol. There are peaks split into triplet peaks and doublet peaks. The molecule is drawn on the spectrum with the peaks and protons are labeled to make the atom to the peak

Figure 1: Proton NMR spectrum of ethanol