Event cameras generate asynchronous, sparse data streams with microsecond temporal resolution, but in moderate-to-high motion scenes they can produce as many as hundreds of millions of events per second, creating significant bandwidth and storage challenges. Lossy compression is therefore essential for practical deployment, yet existing event stream distortion metrics fail to reliably predict compression-induced degradation at the task level, forcing codec optimization to rely on expensive task-specific evaluations. To address this gap, this paper introduces two fundamentally different event compression pipelines: i) an aggregation-based pipeline that converts the event stream into polarity-based histogram frames for compression with the conventional image codec JPEG 2000, and ii) a frame-free point cloud-based pipeline that codes events natively as 3D points using the octree-based codec G-PCC. Both pipelines are then assessed within a unified task-driven evaluation framework that relates event stream distortion to downstream application performance across four representative tasks: i) video reconstruction, ii) object detection, iii) optical flow estimation, and a delay-sensitive task iv) asynchronous feature tracking under a reference-relative protocol. Building on this framework, five classification-based distortion metrics are applied to event compression for the first time, to the best of the authors' knowledge, and benchmarked against existing event stream metrics. Experimental results demonstrate that the proposed metrics reliably predict compression-induced task degradation across different coding frameworks. This demonstrates that event stream distortion assessment can be an efficient alternative to repeated task-specific evaluation, providing direct guidance for the development and optimization of future event data coding solutions.

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