  In the contemporary era of high-precision spectroscopic surveys, led by
projects like DESI, there is an increasing demand for optimizing the extraction
of cosmological information from clustering data. This work conducts a thorough
comparison of various methodologies for modeling the full shape of the
two-point statistics in configuration space. We investigate the performance of
both direct fits (Full-Modeling) and the parameter compression approaches
(ShapeFit and Standard). We utilize the ABACUS-SUMMIT simulations, tailored to
exceed DESI's precision requirements. Particularly, we fit the two-point
statistics of three distinct tracers (LRG, ELG, and QSO), by employing a
Gaussian Streaming Model in tandem with Convolution Lagrangian Perturbation
Theory and Effective Field Theory. We explore methodological setup variations,
including the range of scales, the set of galaxy bias parameters, the inclusion
of the hexadecapole, as well as model extensions encompassing varying $n_s$ and
allowing for $w_0w_a$CDM dark energy model. Throughout these varied
explorations, while precision levels fluctuate and certain configurations
exhibit tighter parameter constraints, our pipeline consistently recovers the
parameter values of the mocks within $1\sigma$ in all cases for a 1-year DESI
volume. Additionally, we compare the performance of configuration space
analysis with its Fourier space counterpart using three models: PyBird, FOLPS
and velocileptors, presented in companion papers. We find good agreement with
the results from all these models.
