i.e., for two angles, normal and 80 degrees with respect to normal surface
For the larger angle (i.e.) 80 degress in your case, you become far more surface senisitive, therefore you are detecting a greater fraction of the electrons originating from the surface layer as opposed to the surface and near surface region observed at normal emission.
Therefore you should see a change in the ratio due to an enhancement of components located towards the surface
To follow David's response, the sampling depth is defined as 3 times the electron Inelastic Mean Free Path (IMFP) multiplied by cos(Theta). This is just 3*IMFP for normal incidence XPS (cos0=1) but is 0.5*(3*IMFP) at 60 degrees. So for example your sampling depth is reduced from 3 nm to 1.5 nm. As David says, if you have a metal with an oxide layer at the surface, you will be sampling less of the metal at 60 degrees compared to oxide, so the oxygen-associated species will increase. You can use the dependence of the intensity of different elements/ chemical species to determine the layer thickness (for thin layers like oxides of course!). And there are some free software (like XPS MultiQuant) to help with this, although it can be done by hand calcs as well (search "XPS thickogram").
So if you have a perfect, uniform and clean sample, there should be no difference between the two (although you usually get a lot less counts so your signal-to-noise will be worse probably), but if there is any depth-related changes you will see this.
Note that the sampling depth / electron inelastic mean free path varies by atom and kinetic energy (so it will change with photon energy and different core levels). See the NIST database of IMFPs. If you're unlucky you will end up measuring different core levels with quite a difference in sampling depth --- so it gets complicated! To avoid a large discrepancy you can choose core levels closer together in binding energy, but obvs this isn't possible for e.g. Mg and Al.
In addition to the above effect related to the mean free path you can also have intensity variations due to forward focusing / scattering, if you have an ordered / crystalline material and sufficient kinetic energy of your electrons. See for example page 94 of Applications of synchrotron radiation (https://books.google.se/books?id=Bv7piP5WU4sC&pg=PA94&lpg=PA94&dq=forward+focusing+back+scattering+photoelectron&source=bl&ots=1rUzm6XNiY&sig=qdlKTW3AHX5wq1Z1x1lB2qciyJw&hl=sv&sa=X&ved=0ahUKEwj19u7RmMPPAhWD3CwKHSaZAXEQ6AEIZDAI#v=onepage&q=forward%20focusing%20back%20scattering%20photoelectron&f=false). This effect is used in the technique known as X-ray photoelectron diffraction (XPD).
Yet another effect is related to the band structure of the material in crystalline materials. However, if you are performing XPS you are usually in the “XPS limit” where you do not see such effects. This limit appears when the phonon broadening of the spectra and the angular averaging in the spectrometer leads to that the measured spectra represent the matrix-element weighted density of states (DOS) of the crystal and the origin of the intensity change with angle is dominated by diffraction effects (as seen in XPD) experiments). But under some circumstances it is possible to probe the bandstructure using higher energies. See for example C. Papp et al. Physical review B 84 (2011) 045433.
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