Registrly cross-references both — 6.5M UK companies and 3.4M LEI-registered entities worldwide — and shows comparative context neither registry gives you alone (e.g. how a company's age ranks against every other company registered in the same town or country).
It's free, built entirely on open government/international data (Companies House OGL, GLEIF CC0), and not affiliated with either registry.
Happy to answer questions about the data, the cross-referencing approach, or anything else.