Modern cellular networks utilizing the long-term evolution (LTE) set of standards face an ever-increasing demand for mobile data from connected devices. Header compression is commonly employed to minimize the overhead for IP-based cellular network traffic. In this paper, we evaluate the three header compression implementations 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 contribution of this article is the performance evaluation of IP Header Compression (IPHC) for UDP and TCP, as well as its evaluation in contrast to the Robust Header Compression (RoHC) methods in a comparative overview for real-world mobile scenarios. Our results show that all implementations have great potential for saving bandwidth in IP-based wireless networks, even under varying channel conditions. While both RoHC versions generally provide more reliable results than IPHC, we find that on a unidirectional channel, IPHC could perform better. However, if a TCP connection is prone to packets reordering (e.g., by retransmissions), IPHC's performance drops drastically, while RoHC's does not exhibit a significant performance impact.