This paper concerns the experimental performance evaluation of three protocols for channel access in underwater acoustic sensor networks. In particular, we consider handshake-free protocols, i.e., solutions for accessing the acoustic channel without mechanisms of pre-emptive channel reservation, aiming at obtaining lower packet latencies while maintaining high throughput. Two of the protocols that we consider, namely, the Traffic-Adaptive Receiver-Synchronized (TARS) protocol, and the Lightweight Stochastic Scheduling (LiSS) protocol, are based on a utility-optimization framework for computing the optimal transmission strategy dynamically. We benchmark the performance of TARS and LiSS to that of ALOHA, which is the exemplary handshake-free protocol. Our experimental evaluation is based on a testbed of four Teledyne Benthos acoustic modems deployed in an outdoor pool filled with water from the ocean. Our results show that the optimization framework of protocols such as TARS and LiSS achieves remarkable performance both in terms of packet delivery ratio, because of a noticeable reduction of interference, and of end-to-end latency, because of considerable shortening of the slot duration.