Bars are a key factor in the long-term evolution of spiral galaxies, in their unique role in redistributing angular momentum and transporting gas and stars on large scales. The Eris-suite simulations are cosmological zoom-in, N-body, smoothed-particle hydrodynamic simulations built to follow the formation and evolution of a Milky Way-sized galaxy across the build-up of the large scale structure. Here we analyse and describe the outcome of two particular simulations taken from the Eris suite – ErisBH and Eris2k – which mainly differ in the prescriptions employed for gas cooling, star formation, and feedback from supernovae and black holes. Our study shows that the enhanced effective feedback in Eris2k, due to the collective effect of the different micro-physics implementations, results in a galaxy which is less massive than its ErisBH counterpart till z ∼ 1. However, when the stellar content is large enough so that global dynamical instabilities can be triggered, the galaxy in Eris2k develops a stronger and more extended bar with respect to ErisBH. We demonstrate that he structural properties and time evolution of the two bars are very different. Our results highlight the importance of accurate sub-grid prescriptions in cosmological zoom-in simulations of the process of galaxy formation and evolution, and the possible use of a statistical sample of barred galaxies to assess the strength of the stellar feedback.