I have tried a few, but am now using HSBC Premier in three countries (up one since last week since I just moved from Barclays to HSBC in one country). HSBC does have purely local service and account managers, who often don't know about the rest of their system. I thus qualified distinctly for France, Jersey, Brazil.

The customer service is excellent everywhere I have used it and transfers are free within their system, that's a big factor for me. The Global View makes it simple to see everything in all countries on one screen, and that is important o me also.

They introduce Premiers to other HSBC locations who always seem anxious to be helpful. They have seminars and give tickets to cultural events and other such perks.

I quit the Private Bank to stay with Premier because the fees were lower and they are much less obtrusive.

The downside: You don't get great rates on anything, so you'll need to use their home brokerage to get reasonable returns. Their advice is no better than anybody else's, so it is self serving and expensive.

If you want credit cards, transactional services and easy movement from one country to another they're better than anybody else because they have the coverage everywhere. if you don't want those things there are probably better places. I want them and I'm very happy with them.