It largely depends on whether you think it likely that the business requirements will evolve in a similar way or not (same business rationale especially as far as codification is concerned)
Of course it means you share account classes (incl CFY flag), account format, and accounting codes (suppliers, customers, taxes etc.)
If you opt for 1 CoA, then you'll only be able to define exceptions - that is accounts restricted to a legal entity (useful possibly for bank accounts)
It also means that profit & loss accounts, fx variance, etc. accounts must be the same as they're currently defined at the CoA level
Same goes for dimensions (which dimensions enabled on which accounts), budget tracking. moreover, if you implement default dimensions at the account level, the same default value will apply for both companies

If you use mainly purchasing & sales for invoicing then having no default tax code may not be such a big issue (it also depends on how many direct journals you have). The biggest issue concerning VAT/GST is that sharing the same revenue / expense accounts will be submitted to VAT/GST that is you can't have an account not submitted to VAT in the UK and submitted to GST in Aus.

If you implement FA then same logic applies here : FA accounts and accounting codes will share the same attributes.

This list may not be exhaustive but is as much as I can think of for the moment