Atmospheric air-filled hollow core (HC) fibers, representing the simplest yet reliable form of gas-filled hollow core fiber, show remarkable nonlinear properties and have several interesting applications such as pulse compression, frequency conversion and supercontinuum generation. Although the propagation of sub-picosecond and few hundred picosecond pulses are well-studied in air-filled fibers, the nonlinear response of air to pulses with a duration of a few picoseconds has interesting features that have not yet been explored fully. Here, we experimentally and theoretically study the nonlinear propagation of ~6 ps pulses in three different types of atmospheric air-filled HC fiber. With this pulse length, we were able to explore different nonlinear characteristics of air at different power levels. Using in-house-fabricated, state-of-the-art HC photonic bandgap, HC tubular and HC Kagomé fibers, we were able to associate the origin of the initial pulse broadening process in these fibers to rotational Raman scattering (RRS) at low power levels. Due to the broadband and low loss transmission window of the HC Kagomé fiber we used, we observed the transition from initial pulse broadening (by RRS) at lower powers, through long-range frequency conversion (2330 cm-1) with the help of vibrational Raman scattering, to broadband (~700 nm) supercontinuum generation at high power levels. To model such a wide range of nonlinear processes in a unified approach, we have implemented a semi-quantum model for air into the generalized nonlinear Schrodinger equation, which surpasses the limits of the common single damping oscillator model in this pulse length regime. The model has been validated by comparison with experimental results and provides a powerful tool for the design, modeling and optimization of nonlinear processes in air-filled HC fibers.