Robotic grippers are increasingly deployed across industrial, collaborative, and aerial platforms, where each embodiment imposes distinct mechanical, energetic, and operational constraints. Established YCB and NIST benchmarks quantify grasp success, force, or timing on a single platform, but do not evaluate cross-embodiment transferability or energy-aware performance, capabilities essential for modern mobile and aerial manipulation. This letter introduces the Cross-Embodiment Gripper Benchmark (CEGB), a compact and reproducible benchmarking suite extending YCB and selected NIST metrics with three additional components: a transfer-time benchmark measuring the practical effort required to exchange embodiments, an energy-consumption benchmark evaluating grasping and holding efficiency, and an intent-specific ideal payload assessment reflecting design-dependent operational capability. Together, these metrics characterize both grasp performance and the suitability of reusing a single gripper across heterogeneous robotic systems. A lightweight self-locking gripper prototype is implemented as a reference case. Experiments demonstrate rapid embodiment transfer (median ~= 17.6 s across user groups), low holding energy for gripper prototype (~= 1.5 J per 10 s), and consistent grasp performance with cycle times of 3.2 - 3.9 s and success rates exceeding 90%. CEGB thus provides a reproducible foundation for cross-platform, energy-aware evaluation of grippers in aerial and manipulators domains.