The Bible describes a splendid empire under Solomon (1 Kings 4-10). The dispute is usually framed as the Low Chronology against the conventional dating, and it's primarily about the absolute dating of tenth-century strata — the political conclusions follow from that. Israel Finkelstein's later dating yields a more modest highland polity; Amihai Mazar's Modified Conventional Chronology allows for something more substantial.
Both scholars work from the same sites — Megiddo, Hazor, Gezer — and date their strata differently, which changes what can be attributed to Solomon. The proposals run along a spectrum rather than between two poles, and "empire" is a word that needs defining before it can be affirmed or denied.
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