Autonomous Underwater Vehicles (AUVs) are a useful tool for science and industry. They significantly reduce the risk to humans in operations in hazardous and high cost situations. The use of multiple AUVs can enhance the operational capabilities by introducing specialisation of AUV capabilities and parallelising task execution. The coordination of the multi-AUV team requires communication among its members. Underwater communications are low bandwidth, high latency and error prone. This paper studies different task allocation strategies for an underwater archaeological inspection scenario under communication constraints. Three different distributed methods are implemented and compared in simulation. The first is a greedy allocation method used as a baseline for comparison. The second is a k-Means based formulation aiming to balance the load among the robots. The third is the linear programming formulation of the multiple travelling salesmen problem. Results are analysed in the scope of mission completion time and the distance travelled by the robots. Results indicate that the k-Means method performs better when communication error rates are lower, while the mTSP method performs better when communication error rates are higher.