Both EE Business and BT Business are part of BT Group. The difference is positioning. EE Business leads with mobile and bundles broadband, Microsoft 365 and security on top. BT Business leads with broadband and hosted voice, with mobile sold as an add-on. For a typical 1 to 50-person business where most people work from a laptop and a phone, EE Business is the simpler choice and usually the cheaper one. For businesses that need hosted PBX, multi-site Ethernet or cyber-security with a managed-service wrap, BT Business has the deeper feature set.
If you are picking between them and the team is mostly mobile-and-Microsoft-365, start with EE Business. If you are picking between them and the team is mostly desk-phone-and-leased-line, start with BT Business. Both share the same Openreach network, the same SLAs at the leased-line tier, and the same complaints process via CISAS.