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Open datasets and benchmarks for entity-level carbon-emission prediction remain fragmented across access, scale, granularity, and evaluation. We introduce GHGbench, an open dataset and benchmark for company- and building-level greenhouse-gas prediction. The company track contains 32,000+ company-year records from 12,000+ firms with Scope 1+2 and Scope 3 disclosures and financial/sectoral signals; the building track harmonises 491,591 building-year records from 13 open sources into a single schema across 26 metropolitan areas (10 U.S., 15 Australian, 1 Singaporean), with climate covariates and multimodal remote-sensing embeddings. GHGbench defines canonical splits with in-distribution and cross-region/city transfer as primary tasks and temporal hold-out plus short-horizon forecasting as supplementary appendix evidence; headline baselines span gradient-boosted trees, a tabular foundation model, MLP, FT-Transformer, and multimodal fusion, with an LLM panel as auxiliary, all evaluated under multi-seed paired-bootstrap tests. Three benchmark-level findings emerge: (i) building emissions are structurally harder than company emissions; (ii) the in-distribution to out-of-distribution gap dwarfs any within-model gap across both the company track and the building track, and a tabular foundation model is, to our knowledge, the first baseline to open a paired-bootstrap-significant gap over tuned trees on a multi-city building-emissions task; (iii) multimodal remote-sensing embeddings help precisely where tabular generalisation breaks. GHGbench also exposes catastrophic city transfer and the sector-factor lookup ceiling as systematic failure modes. Code and reconstruction recipes are available at GHGbench.