Hadron therapy, which employs particles such as protons and carbon-ions, is a promising method of cancer treatment due to its unique ability to deliver maximum energy at the Bragg peak near the tumor, sparing surrounding healthy tissue. Ionoacoustic waves, generated by thermal expansion from electronic collisions and localized heating, can be detected to optimize dose delivery and verify particle range, thus improving treatment precision. These waves offer a unique opportunity for comparative studies of different particle therapies. In this study, a mathematical model and computational simulations are used to compare the characteristics of ionoacoustic waves generated in tissue by proton and carbon-ion beams. In particular, we assess the impact of the nuclear fragmentation tail on the ionoacoustic signals generated in carbon-ion therapy. Our approach will allow us to make some important observations to study the comparative effects of proton and carbon-ion therapy. The aim of this work is to perform a comprehensive comparative analysis of ionoacoustic waves from proton and carbon-ion treatments, focusing on their potential for in-vivo range verification. This research addresses the current gap in understanding the use of ionoacoustic signals for range verification in ion beam therapy, which is critical given the growing clinical application of carbon ion therapy and its under-explored acoustic properties. This study pioneers the feasibility of using acoustic imaging from carbon-ion beams to detect the Bragg peak position and measure tumor dose in real-time. Carbon-ion dose mapping and relative biological effectiveness (RBE) assessment can be facilitated by real-time signal monitoring. Our study aims to significantly advance the field by addressing the lack of a verification technique for carbon-ion beams, focusing on the considerable impact of the nuclear fragmentation tail on ionoacoustic signal waveforms, which provides crucial insights into the unique energy deposition properties of carbon-ions.