To the best of my knowledge, you can't give better VAT conditions to a business customer without having checked the EU VAT number with EU VAT server (which CBSubs allows, and that part works). Just getting any company number and VAT number is not enough to not collect VAT per EU VAT rules (check with your tax lawyer/consultant).
You need to set "Methods to validate that the customer is a business (B2) for this tax" to "EU VAT: Online check with EU VAT Server" (NOT "Company and VAT in invoice"), and fill-in your EU VAT number below. That setting works fine, and is to my knowledge the only one to use in Europe (it's even written "recommended for EU sellers" in the drop-down choice).
Additionally, for the country rates selection to work, your seller country (and province and post code) must be selected in General CBSubs settings, integrations, tax tab.