Large language models (LLMs) have demonstrated strong performance on coding and reasoning benchmarks; however, their ability to solve graph-structured machine learning problems remains largely unexplored. In particular, no benchmark currently evaluates whether LLMs can autonomously solve end-to-end Graph Neural Network (GNN) coding tasks under realistic competition settings. To address this gap, this paper introduces GNN-CB, the first competition-based benchmark for evaluating both humans and LLMs on GNN coding tasks. GNN-CB consists of 18 curated competitions spanning node-, edge-, and graph-level prediction across diverse graph categories, domains, and difficulty tiers. All submissions are evaluated through a unified automated pipeline with hidden test sets and standardized scoring. Human participants solve tasks under controlled competition constraints, while LLMs are evaluated using a frozen zero-shot prompting protocol based on a plan-then-code paradigm with bounded execute-and-repair loops. The benchmark additionally supports both non-agent and autonomous agent-based evaluation within the same protocol. Under our evaluated protocol, LLMs rarely match Human Top performance and show less stable performance across competitions. No single model dominates: a few competitions are won by LLMs, yet humans still hold the top score on most tasks. We release GNN-CB as a living benchmark with automated evaluation infrastructure, dynamic leaderboards, and reproducible execution pipelines. Beyond benchmarking, GNN-CB provides a practice-oriented resource for studying GNN implementation across progressively diverse graph-learning tasks. The benchmark and evaluation framework are publicly available at https://basiralab.github.io/GNN-CB/.