One difference for example is that for EU Presidents Club members benefits are can only given in the following countries (source: https://www.avis.co.uk/your-avis/avis-loyalty)

Austria
Belgium
Czech Republic
Denmark
Finland
France
Germany
Greece
Ireland
Iceland
Italy
Luxembourg
Netherlands
Norway
Poland
Portugal
South Africa
Spain
Sweden
Switzerland
Turkey
United Kingdom


I came across this because when logging in into the US app it shows for me only Preferred as status. When emailing the customer service they told me that the programs are different between Europe and US. well in the US they don't seem to know because I got upgrades but usually only after asking.