What are the pros and cons of angular cross-correlation in real space and harmonic space?

In observational cosmology people often measure and model cross-correlations between different tracer maps. There are generally two ways to measure cross-correlations:

1. in real space (two-point function):

$$
xi^{uv}(theta) equiv leftlangle u(boldsymbol{theta’}) v(boldsymbol{theta’}+boldsymbol{theta}) rightrangle_{boldsymbol{theta}’}
$$

2. in harmonic space (angular power spectrum)

$$
xi^{uv}(theta)=int d ell frac{ell}{2 pi} C_{ell}^{uv} J_{0}(ell theta)
$$

I’m wondering in the sense of measurements, modelling, systematics, etc, what are the pros and cons of these two methods?