Modern cellular networks utilizing the long-term evolution (LTE) set of standards face an ever-increasing demand for mobile data from connected devices and header compression is employed to minimize the overhead for IP-based cellular network traffic. In this paper, we evaluate the three implementations of header compressions used by these networks with respect to their potential throughput increase and complexity for different mobile service scenarios over wireless IP networks. Specifically, we consider header compression as defined by (i) IP Header Compression (RFC 2507), (ii) Robust Header Compression version 1 (RFC 3095), and (iii) the recently updated Robust Header Compression version 2 (RFC 5225) with TCP/IP profile (RFC 6846). The novelty of this paper is the presentation of the performance evaluation of IP Header Compression for UDP and TCP, as well as a comparison between the two compression methods. Our findings show that all implementations have great potential for saving bandwidth in IP-based wireless networks, even under varying channel conditions. While the RoHC versions generally provide more reliable results than IPHC, we find that on a unidirectional channel, IPHC could perform better.