One of the current challenges of planet formation theory is to explain the enrichment of observed exoplanetary atmospheres. Past studies have focused on scenarios where either pebbles or planetesimals were the heavy element enrichment's drivers, we combine here both approaches to understand whether the composition of a planet can constrain its formation pathway. We study three different formation scenarios: pebble accretion, pebble accretion with planetesimal formation, combined pebble and planetesimal accretion. We use the chemcomp code to perform semi-analytical 1D simulations of protoplanetary discs, including viscous evolution, pebble drift, and simple chemistry to simulate the growth of planets from planetary embryos to gas giants as they migrate through the disc, while tracking their composition. Our simulations confirm that the composition of the planetary atmosphere is dominated by the accretion of gas enriched by inward drifting and evaporating pebbles. Including planetesimal formation hinders the enrichment, because the pebbles locked into planetesimals cannot evaporate and enrich the disc. This results in a big drop of the accreted heavy elements both in the planetesimal formation and accretion case, proving that planetesimal formation needs to be inefficient in order to explain planets with high heavy element content. Accretion of planetesimals enhances the refractory component of the atmosphere, leading to low volatile to refractory ratios, contrary to the pure pebble scenario. Such low volatile to refractory ratios can also be achieved by planets migrating in the inner disc in pure pebble scenario. Distinguishing these two scenarios requires knowledge about the planet's atmospheric C/H and O/H ratios, which are higher for pure pebble accretion. Therefore, a detailed knowledge of the composition of planetary atmospheres could help to constrain the planet's formation pathway.