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From my personal experience getting verified on casinos and also on other kind of services, it would seem to me that passports have more value and weight when comes to making sure the casino can be sure you are summiting actual information which is related to you as a person and there is nothing fishy going on.
I have got that impression, because in my country, our national identity cards are very cheap and made of low quality material, they do not have any security element whatsoever. So in the eyes of casinos is better if gamblers can send them passport pictures, which follow a minimum of international standards and they are also harder to counterfeit when compared to identity cards.
I have used identity cards, but since I have managed to get a passport on my hands, I have opted to use it for gambling and non-gambling verification on internet.
You're right, the use of an international passport has much weight in making the process more faster, for those that has one because most of these sites often accept it more than any other means of identification, another document I think is more recommended is driver's license, all these request for verification may take extra working days in case they need to cross check and very any of these documents and the process, then another thing that may cause delay is when it's over the weekend or if there are many numbers of unattended users to on queue to be verified, it may take longer.
When we talking about verification on casino what we should know is that most casinos make this process very easy and fast as long as the gambler provides the accurate means of identification for such process, the mode of application and documentation matters in how fast the process can be, in most Cases I have never experienced time longer than 15 minutes to get verified using my driver's license in most cases.