Broadband mobile networks have rapidly evolved over the last years. The unique environment they operate, however, sets new challenges for the Transmission Control Protocol (TCP). In this paper, we study the impact of Long Term Evolution (LTE) handover on TCP performance with different TCP congestion control algorithms and in a wide range of networks settings, including different handover types, random channel errors and support of error correction at lower layers. Our results suggest that the congestion control algorithms employed by TCP variants during the LTE X2 handover have different impacts on TCP performance. In particular CUBIC, Scalable TCP and BIC-TCP achieve high goodput and fast window convergence in available channel capacity after LTE X2 handover. In environments involving packet drops that are not corrected at lower layers and single errors with high probability, all TCP variants exhibit very low performance levels. Finally, in terms of fairness, our results identify fairness issues among TCP flows with different Bandwidth Delay Products (BDP), with CUBIC offering the best results.